Search results for: predictive equations

Authors: Toshiyuki Satoh, Hiroki Hara, Naoki Saito, Jun-ya Nagase, Norihiko Saga

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This paper addresses a control system design for a table drive system based on the disturbance observer (DOB)-based predictive functional critical control (PFCC). To empower the previously developed DOB-based PFC to handle constraints on controlled outputs, we propose to take a critical control approach. To this end, we derive the transfer function representation of the PFC controller, and yield a detailed design procedure. The effectiveness of the proposed method is confirmed through an experimental evaluation.

Keywords: critical control, disturbance observer, mechatronics, motion control, predictive functional control, table drive systems

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Abdelhalim Kessal

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This paper treats a design of combined control of a single phase power factor correction (PFC). The strategy of the proposed control is based on two parts, the first, for the outer loop (DC output regulated voltage), and the second govern the input current of the converter in order to achieve a sinusoidal form in phase with the grid voltage. Two kinds of regulators are used, Fuzzy controller for the outer loop and predictive controller for the inner loop. The controllers are verified and discussed through simulation under MATLAB/Simulink platform. Also an experimental confirmation is applied. Results present a high dynamic performance under various parameters changes.

Keywords: boost converter, harmonic distortion, Fuzzy, predictive, unity power factor

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Authors: Irtaza M. Syed, Kaamran Raahemifar

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This paper presents a model predictive control (MPC) of a utility interactive three phase inverter (TPI) for a photovoltaic (PV) system at commercial level. The proposed model uses phase locked loop (PLL) to synchronize TPI with the power electric grid (PEG) and performs MPC control in a dq reference frame. TPI model consists of boost converter (BC), maximum power point tracking (MPPT) control, and a three leg voltage source inverter (VSI). Operational model of VSI is used to synthesize sinusoidal current and track the reference. Model is validated using a 35.7 kW PV system in Matlab/Simulink. Implementation and results show simplicity and accuracy, as well as reliability of the model.

Keywords: model predictive control, three phase voltage source inverter, PV system, Matlab/simulink

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: Ronit Chakraborty, Sugata Banerji

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There has been a marked increase in the reported prevalence of Autism Spectrum Disorder (ASD) among children in the US over the past two decades. This research has analyzed the growth in state-level ASD prevalence against 45 different potentially explanatory factors, including socio-economic, demographic, healthcare, public policy, and political factors. The goal was to understand if these factors have adequate predictive power in modeling the differential growth in ASD prevalence across various states and if they do, which factors are the most influential. The key findings of this study include (1) the confirmation that the chosen feature set has considerable power in predicting the growth in ASD prevalence, (2) the identification of the most influential predictive factors, (3) given the nature of the most influential predictive variables, an indication that a considerable portion of the reported ASD prevalence differentials across states could be attributable to over and under diagnosis, and (4) identification of Florida as a key outlier state pointing to a potential under-diagnosis of ASD there.

Keywords: autism spectrum disorder, clustering, machine learning, predictive modeling

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Authors: Archit Yajnik, Rustam Ali

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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.

Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation

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Authors: Jun-ya Nagase, Toshiyuki Satoh, Norihiko Saga, Koichi Suzumori

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In recent years, Japanese society has been aging, engendering a labour shortage of young workers. Robots are therefore expected to perform tasks such as rehabilitation, nursing elderly people, and day-to-day work support for elderly people. The pneumatic balloon actuator is a rubber artificial muscle developed for use in a robot hand in such environments. This actuator has a long stroke, and a high power-to-weight ratio compared with the present pneumatic artificial muscle. Moreover, the dynamic characteristics of this actuator resemble those of human muscle. This study evaluated characteristics of force control of balloon actuator using a predictive functional control (PFC) system with disturbance observer. The predictive functional control is a model-based predictive control (MPC) scheme that predicts the future outputs of the actual plants over the prediction horizon and computes the control effort over the control horizon at every sampling instance. For this study, a 1-link finger system using a pneumatic balloon actuator is developed. Then experiments of PFC control with disturbance observer are performed. These experiments demonstrate the feasibility of its control of a pneumatic balloon actuator for a robot hand.

Keywords: disturbance observer, pneumatic balloon, predictive functional control, rubber artificial muscle

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Authors: Mais Khader, Xingjie Wei

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This research sheds light on female entrepreneurs by providing new insights on the survival predictions of companies led by females in the UK. This study aims to build a predictive machine learning model of the survival of female-led & co-led small & medium enterprises (SMEs) in the UK over the period 2000-2020. The predictive model built utilised a combination of financial and non-financial features related to both companies and their directors to predict SMEs' survival. These features were studied in terms of their contribution to the resultant predictive model. Five machine learning models are used in the modelling: Decision tree, AdaBoost, Naïve Bayes, Logistic regression and SVM. The AdaBoost model had the highest performance of the five models, with an accuracy of 73% and an AUC of 80%. The results show high feature importance in predicting companies' survival for company size, management experience, financial performance, industry, region, and females' percentage in management.

Keywords: company survival, entrepreneurship, females, machine learning, SMEs

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Authors: Magdi M. Nabi, Ding-Li Yu

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This paper presents a neural network based model predictive control (MPC) strategy to control a strongly exothermic reaction with complicated nonlinear kinetics given by Chylla-Haase polymerization reactor that requires a very precise temperature control to maintain product uniformity. In the benchmark scenario, the operation of the reactor must be guaranteed under various disturbing influences, e.g., changing ambient temperatures or impurity of the monomer. Such a process usually controlled by conventional cascade control, it provides a robust operation, but often lacks accuracy concerning the required strict temperature tolerances. The predictive control strategy based on the RBF neural model is applied to solve this problem to achieve set-point tracking of the reactor temperature against disturbances. The result shows that the RBF based model predictive control gives reliable result in the presence of some disturbances and keeps the reactor temperature within a tight tolerance range around the desired reaction temperature.

Keywords: Chylla-Haase reactor, RBF neural network modelling, model predictive control, semi-batch reactors

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Authors: Abderrahmane El Kachani, El Mahjoub Chakir, Anass Ait Laachir, Abdelhamid Niaaniaa, Jamal Zerouaoui, Tarik Jarou

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This paper presents a wind turbine based on the doubly fed induction generator (DFIG) connected to the utility grid through a shunt active power filter (SAPF). The whole system is controlled by a double nonlinear predictive controller (DNPC). A Taylor series expansion is used to predict the outputs of the system. The control law is calculated by optimization of the cost function. The first nonlinear predictive controller (NPC) is designed to ensure the high performance tracking of the rotor speed and regulate the rotor current of the DFIG, while the second one is designed to control the SAPF in order to compensate the harmonic produces by the three-phase diode bridge supplied by a passive circuit (rd, Ld). As a result, we obtain sinusoidal waveforms of the stator voltage and stator current. The proposed nonlinear predictive controllers (NPCs) are validated via simulation on a 1.5 MW DFIG-based wind turbine connected to an SAPF. The results obtained appear to be satisfactory and promising.

Keywords: wind power, doubly fed induction generator, shunt active power filter, double nonlinear predictive controller

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Authors: Bruk Gebregziabher

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The safe and efficient operation of Autonomous Mobile Robots (AMRs) in complex environments, such as manufacturing, logistics, and agriculture, necessitates accurate multiobject tracking and predictive collision avoidance. This paper presents algorithms and techniques for addressing these challenges using Lidar sensor data, emphasizing ensemble Kalman filter. The developed predictive collision avoidance algorithm employs the data provided by lidar sensors to track multiple objects and predict their velocities and future positions, enabling the AMR to navigate safely and effectively. A modification to the dynamic windowing approach is introduced to enhance the performance of the collision avoidance system. The overall system architecture encompasses object detection, multi-object tracking, and predictive collision avoidance control. The experimental results, obtained from both simulation and real-world data, demonstrate the effectiveness of the proposed methods in various scenarios, which lays the foundation for future research on global planners, other controllers, and the integration of additional sensors. This thesis contributes to the ongoing development of safe and efficient autonomous systems in complex and dynamic environments.

Keywords: autonomous mobile robots, multi-object tracking, predictive collision avoidance, ensemble Kalman filter, lidar sensors

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Authors: Sofiane Bououden, Ilyes Boulkaibet

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In this paper, a robust fault-tolerant predictive control (FTPC) strategy is proposed for systems with linear parameter varying (LPV) models and input constraints subject to sensor faults. Generally, virtual observers are used for improving the observation precision and reduce the impacts of sensor faults and uncertainties in the system. However, this type of observer lacks certain system measurements which substantially reduce its accuracy. To deal with this issue, a real observer is then designed based on the virtual observer, and consequently a real observer-based robust predictive control is designed for polytopic LPV systems. Moreover, the proposed observer can entirely assure that all system states and sensor faults are estimated. As a result, and based on both observers, a robust fault-tolerant predictive control is then established via the Lyapunov method where sufficient conditions are proposed, for stability analysis and control purposes, in linear matrix inequalities (LMIs) form. Finally, simulation results are given to show the effectiveness of the proposed approach.

Keywords: linear parameter varying systems, fault-tolerant predictive control, observer-based control, sensor faults, input constraints, linear matrix inequalities

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Authors: Novutry Siregar, Afdal, Emilzon Taslim

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Hyaline Membrane Disease (HMD) is the main cause of respiratory failure in preterm neonates caused by surfactant deficiency. Nasal Continuous Positive Airway Pressure (NCPAP) is the therapy for HMD. The success of therapy is determined by gestational age, birth weight, HMD grade, time of NCAP administration, and time of breathing frequency recovery. The aim of this research is to identify the predictive factor of NCPAP therapy success in preterm neonates with HMD. This study used a cross-sectional design by using medical records of patients who were treated in the Perinatology of the Pediatric Department of Dr. M. Djamil Padang Central Hospital from January 2015 to December 2017. The samples were eighty-two neonates that were selected by using the total sampling technique. Data analysis was done by using the Chi-Square Test and the Multiple Logistic Regression Prediction Model. The results showed the success rate of NCPAP therapy reached 53.7%. Birth weight (p = 0.048, OR = 3.34 95% CI 1.01-11.07), HMD grade I (p = 0.018, OR = 4.95 CI 95% 1.31-18.68), HMD grade II (p = 0.044, OR = 5.52 95% CI 1.04-29.15), and time of breathing frequency recovery (p = 0,000, OR = 13.50 95% CI 3.58-50, 83) are the predictive factors of NCPAP therapy success in preterm neonates with HMD. The most significant predictive factor is the time of breathing frequency recovery.

Keywords: predictive factors, the success of therapy, NCPAP, preterm neonates, HMD

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Authors: Minas Balyan

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Nowadays X-ray nonlinear diffraction and nonlinear effects are investigated due to the presence of the third generation synchrotron sources and XFELs. X-ray third order nonlinear dynamical diffraction is considered as well. Using the nonlinear model of the usual visible light optics the third-order nonlinear Takagi’s equations for monochromatic waves and the third-order nonlinear time-dependent dynamical diffraction equations for X-ray pulses are obtained by the author in previous papers. The obtained equations show, that even if the Fourier-coefficients of the linear and the third order nonlinear susceptibilities are zero (forbidden reflection), the dynamical diffraction in the nonlinear case is related to the presence in the nonlinear equations the terms proportional to the zero order and the second order nonzero Fourier coefficients of the third order nonlinear susceptibility. Thus, in the third order nonlinear Bragg diffraction case a nonlinear analogue of the well-known Renninger effect takes place. In this work, the 'third order nonlinear Renninger effect' is considered theoretically.

Keywords: Bragg diffraction, nonlinear Takagi’s equations, nonlinear Renninger effect, third order nonlinearity

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Authors: Taiki Baba, Tomoaki Hashimoto

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The random dither quantization method enables us to achieve much better performance than the simple uniform quantization method for the design of quantized control systems. Motivated by this fact, the stochastic model predictive control method in which a performance index is minimized subject to probabilistic constraints imposed on the state variables of systems has been proposed for linear feedback control systems with random dither quantization. In other words, a method for solving optimal control problems subject to probabilistic state constraints for linear discrete-time control systems with random dither quantization has been already established. To our best knowledge, however, the feasibility of such a kind of optimal control problems has not yet been studied. Our objective in this paper is to investigate the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization. To this end, we provide the results of numerical simulations that verify the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization.

Keywords: model predictive control, stochastic systems, probabilistic constraints, random dither quantization

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Authors: Faruk Aras, Melih Inal, Tansel Cinar

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The coordination of airport staff especially in the operations and maintenance departments is important for the airport operation. As a result, this coordination will increase the efficiency in all operation. Therefore, a Collaborative Decision-Making (CDM) system targets on improving the overall productivity of all operations by optimizing the use of resources and improving the predictability of actions. Enlarged productivity can be of major benefit for all airport operations. It also increases cost-efficiency. This study explains how predictive maintenance using IoT (Internet of Things), predictive operations and the statistical data such as Mean Time To Failure (MTTF) improves airport terminal operations and utilize airport terminal equipment in collaboration with collaborative decision making system/Airport Operation Control Center (AOCC). Data generated by the predictive maintenance methods is retrieved and analyzed by maintenance managers to predict when a problem is about to occur. With that information, maintenance can be scheduled when needed. As an example, AOCC operator would have chance to assign a new gate that towards to this gate all the equipment such as travellator, elevator, escalator etc. are operational if the maintenance team is in collaboration with AOCC since maintenance team is aware of the health of the equipment because of predictive maintenance methods. Applying predictive maintenance methods based on analyzing the health of airport terminal equipment dramatically reduces the risk of downtime by on time repairs. We can classify the categories as high priority calls for urgent repair action, as medium priority requires repair at the earliest opportunity, and low priority allows maintenance to be scheduled when convenient. In all cases, identifying potential problems early resulted in better allocation airport terminal resources by AOCC.

Keywords: airport, predictive maintenance, collaborative decision-making system, Airport Operation Control Center (AOCC)

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Julian Thrash, Douglas Folk, Michael Ciracy, Audrey C. Tseng, Kristen M. Stromsodt, Amber Younggren, Christopher Maciolek

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The cardiopulmonary system is comprised of the heart, lungs, and many dynamic feedback mechanisms that control its function based on a multitude of variables. The next generation of cardiopulmonary medical devices will involve adaptive control and smart pacing techniques. However, testing these smart devices on living systems may be unethical and exceedingly expensive. As a solution, a comprehensive computational model of the cardiopulmonary system was implemented in Simulink. The model contains over 240 state variables and over 100 equations previously described in a series of published articles. Simulink was chosen because of its ease of introducing machine learning elements. Initial results indicate that physiologically correct waveforms of pressures and volumes were obtained in the simulation. With the development of a comprehensive computational model, we hope to pioneer the future of predictive medicine by applying our research towards the initial stages of smart devices. After validation, we will introduce and train reinforcement learning agents using the cardiopulmonary model to assist in adaptive control system design. With our cardiopulmonary model, we will accelerate the design and testing of smart and adaptive medical devices to better serve those with cardiovascular disease.

Keywords: adaptive control, cardiopulmonary, computational model, machine learning, predictive medicine

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Authors: Gayathri Sadanala, Shibam Pokhrel, Owen Murphy

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In the ever-evolving landscape of education, Virtual Reality (VR) environments offer a promising avenue for enhancing student engagement and learning experiences. However, understanding and predicting student behavior within these immersive settings remain challenging tasks. This paper presents a comprehensive study on the predictive modeling of student behavior in VR using machine learning techniques. We introduce a rich data set capturing student interactions, movements, and progress within a VR orientation program. The dataset is divided into training and testing sets, allowing us to develop and evaluate predictive models for various aspects of student behavior, including engagement levels, task completion, and performance. Our machine learning approach leverages a combination of feature engineering and model selection to reveal hidden patterns in the data. We employ regression and classification models to predict student outcomes, and the results showcase promising accuracy in forecasting behavior within VR environments. Furthermore, we demonstrate the practical implications of our predictive models for personalized VR-based learning experiences and early intervention strategies. By uncovering the intricate relationship between student behavior and VR interactions, we provide valuable insights for educators, designers, and developers seeking to optimize virtual learning environments.

Keywords: interaction, machine learning, predictive modeling, virtual reality

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Authors: T. Bouchabchoub, A. Bendahmane, A. Haouriqui, N. Attou

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This paper presents simulation results of Forex predicting model equations in order to give approximately a prevision of interest rates. First, Hall-Taylor (HT) equations have been used with Taylor rule (TR) to adapt them to European and American Forex Markets. Indeed, initial Taylor Rule equation is conceived for all Forex transactions in every States: It includes only one equation and six parameters. Here, the model has been used with Hall-Taylor equations, initially including twelve equations which have been reduced to only three equations. Analysis has been developed on the following base macroeconomic variables: Real change rate, investment wages, anticipated inflation, realized inflation, real production, interest rates, gap production and potential production. This model has been used to specifically study the impact of an inflation shock on macroeconomic director interest rates.

Keywords: interest rate, Forex, Taylor rule, production, European Central Bank (ECB), Federal Reserve System (FED).

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Ho-Won Jung, Donghun Lee, Hyung-Jin Kim

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Predictive analytics (data analysis) uses a subset of measurements (the features, predictor, or independent variable) to predict another measurement (the outcome, target, or dependent variable) on a single person or unit. It applies empirical methods in statistics, operations research, and machine learning to predict the future, or otherwise unknown events or outcome on a single or person or unit, based on patterns in data. Most analyses of metabolic syndrome are not predictive analytics but statistical explanatory studies that build a proposed model (theory building) and then validate metabolic syndrome predictors hypothesized (theory testing). A proposed theoretical model forms with causal hypotheses that specify how and why certain empirical phenomena occur. Predictive analytics and explanatory modeling have their own territories in analysis. However, predictive analytics can perform vital roles in explanatory studies, i.e., scientific activities such as theory building, theory testing, and relevance assessment. In the context, this study is to demonstrate how to use our predictive analytics to support theory building (i.e., hypothesis generation). For the purpose, this study utilized a big data predictive analytics platform TM based on a co-occurrence graph. The co-occurrence graph is depicted with nodes (e.g., items in a basket) and arcs (direct connections between two nodes), where items in a basket are fully connected. A cluster is a collection of fully connected items, where the specific group of items has co-occurred in several rows in a data set. Clusters can be ranked using importance metrics, such as node size (number of items), frequency, surprise (observed frequency vs. expected), among others. The size of a graph can be represented by the numbers of nodes and arcs. Since the size of a co-occurrence graph does not depend directly on the number of observations (transactions), huge amounts of transactions can be represented and processed efficiently. For a demonstration, a total of 13,254 metabolic syndrome training data is plugged into the analytics platform to generate rules (potential hypotheses). Each observation includes 31 predictors, for example, associated with sociodemographic, habits, and activities. Some are intentionally included to get predictive analytics insights on variable selection such as cancer examination, house type, and vaccination. The platform automatically generates plausible hypotheses (rules) without statistical modeling. Then the rules are validated with an external testing dataset including 4,090 observations. Results as a kind of inductive reasoning show potential hypotheses extracted as a set of association rules. Most statistical models generate just one estimated equation. On the other hand, a set of rules (many estimated equations from a statistical perspective) in this study may imply heterogeneity in a population (i.e., different subpopulations with unique features are aggregated). Next step of theory development, i.e., theory testing, statistically tests whether a proposed theoretical model is a plausible explanation of a phenomenon interested in. If hypotheses generated are tested statistically with several thousand observations, most of the variables will become significant as the p-values approach zero. Thus, theory validation needs statistical methods utilizing a part of observations such as bootstrap resampling with an appropriate sample size.

Keywords: explanatory modeling, metabolic syndrome, predictive analytics, theory building

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Issam M Hajjaji, Adel Tajoury, Salah R Benhamid

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The MENA region has the highest prevalence of diabetes in the world. Various risk scores were developed, not all appropriate locally. The objective of this study is to apply the FINDRISC Score to adult Libyan males to determine its significance, sensitivity, specificity and Positive Predictive Values as an initial screening tool for type 2 diabetes, and suggest a cut-off point. Methods: 600 subjects answered the questionnaire at their place of work, and their waist, weight, height & BP were measured. Thereafter, after excluding those with known diabetes, an Oral Glucose Tolerance Test was done. Results: 414 subjects aged 19-78 completed the questionnaire and tests. 35 (8.4%) had impaired glucose tolerance (IGT) and 13 (3.1%) had diabetes (DM). The AUC-ROC for IGT was 0.614 (95% CI: 0.527-0.701), for DM 0.810 (95% CI: 0.709-0.911) and for both 0.689 (95% CI: 0.609-0.769). The Positive Predictive Value for a cut-off score of 5 were 15.5%, 11.7% & 5.7% for both conditions combined, prediabetes & diabetes respectively. The equivalent values for a cut-off score of 8 were 16.1%, 9.0% & 7.7%. The Negative Predictive Values were uniformly above 90%. Conclusions & Recommendations: The FINDRISC Score had a low predictive value for dysglycaemia in this sample and performed at a level of significance for IGT that is similar to other MENA countries, but did better for DM. A larger sample that included women is suggested, with a view of adjusting the Score to suit the local population.

Keywords: diabetes, FINDRISK, Libya, prediabetes

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Gaspar J. Machado, Stéphane Clain, Raphael Loubère

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The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part.

Keywords: Euler equations, finite volume, MOOD, steady-state

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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