Search results for: prediction equations

Authors: Zhou Yang, Heli Sun, Jianbin Huang, Jizhong Zhao, Shaojie Qiao

Abstract:

Traffic prediction is essential in a multitude of ways in modern urban life. The researchers of earlier work in this domain carry out the investigation chiefly with two major focuses: (1) the accurate forecast of future values in multiple time series and (2) knowledge extraction from spatial-temporal correlations. However, two key considerations for traffic prediction are often missed: the completeness of raw data and the full context of the prediction timestamp. Concentrating on the two drawbacks of earlier work, we devise an approach that can address these issues in a two-phase framework. First, we utilize the raw trajectories to a greater extent through building a VLA table and data compression. We obtain the intra-trajectory features with graph-based encoding and the intertrajectory ones with a grid-based model and the technique of back projection that restore their surrounding high-resolution spatial-temporal environment. To the best of our knowledge, we are the first to study direct feature extraction from raw trajectories for traffic prediction and attempt the use of raw data with the least degree of reduction. In the prediction phase, we provide a broader context for the prediction timestamp by taking into account the information that are around it in the training dataset. Extensive experiments on several well-known datasets have verified the effectiveness of our solution that combines the strength of raw trajectory data and prediction context. In terms of performance, our approach surpasses several state-of-the-art methods for traffic prediction.

Keywords: traffic prediction, raw data utilization, context building, data reduction

Procedia PDF Downloads 95

Authors: Mohammad Zavid Parvez, Manoranjan Paul

Abstract:

A seizure prediction method is proposed by extracting global features using phase correlation between adjacent epochs for detecting relative changes and local features using fluctuation/deviation within an epoch for determining fine changes of different EEG signals. A classifier and a regularization technique are applied for the reduction of false alarms and improvement of the overall prediction accuracy. The experiments show that the proposed method outperforms the state-of-the-art methods and provides high prediction accuracy (i.e., 97.70%) with low false alarm using EEG signals in different brain locations from a benchmark data set.

Keywords: Epilepsy, seizure, phase correlation, fluctuation, deviation.

Procedia PDF Downloads 441

Authors: Gonzalez Carlos, Martinez Fransisco

Abstract:

The creation of a seismic prediction model that considers all the regional variations and perfectly adjusts its results to the response spectra is very complicated. To achieve statistically acceptable results, it is necessary to process a sufficiently robust data set, and even if high efficiencies are achieved, this model will only work properly in this region. However, when using it in other regions, differences are found due to different parameters that have not been calibrated to other regions, such as the site effect. The fact that impedance contrasts, as well as other factors belonging to the site, have a great influence on the local response is well known, which is why this work, using the residual method, is intended to establish a regional calibration of the corresponding parameters site effect for the Spain region in the global GMPM BSSA 14.

Keywords: GMPM, seismic prediction equations, residual method, response spectra, impedance contrast

Procedia PDF Downloads 62

Authors: Hary Aprianto Wijaya Siahaan, Bayu Edo Pratama

Abstract:

Sea fishery's potential to become one of the nation's assets which very contributed to Indonesia's economy. This fishery potential not in spite of the availability of the chlorophyll in the territorial waters of Indonesia. The research was conducted using three methods, namely: statistics, comparative and analytical. The data used include MODIS sea temperature data imaging results in Aqua satellite with a resolution of 4 km in 2002-2015, MODIS data of chlorophyll-a imaging results in Aqua satellite with a resolution of 4 km in 2002-2015, and Imaging results data ASCAT on MetOp and NOAA satellites with 27 km resolution in 2002-2015. The results of the processing of the data show that the incidence of upwelling in the south of East Java Sea began to happen in June identified with sea surface temperature anomaly below normal, the mass of the air that moves from the East to the West, and chlorophyll-a concentrations are high. In July the region upwelling events are increasingly expanding towards the West and reached its peak in August. Chlorophyll-a concentration prediction using multiple linear regression equations demonstrate excellent results to chlorophyll-a concentrations prediction in 2002 until 2015 with the correlation of predicted chlorophyll-a concentration indicate a value of 0.8 and 0.3 with RMSE value. On the chlorophyll-a concentration prediction in 2016 indicate good results despite a decline in the value of the correlation, where the correlation of predicted chlorophyll-a concentration in the year 2016 indicate a value 0.6, but showed improvement in RMSE values with 0.2.

Keywords: satellite, sea surface temperature, upwelling, wind stress

Procedia PDF Downloads 129

Authors: Zahid Ullah, Atlas Khan

Abstract:

The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

Procedia PDF Downloads 27

Authors: Jeena R. S., Sukesh Kumar A.

Abstract:

Stroke is one of the major reasons of adult disability and morbidity in many of the developing countries like India. Early diagnosis of stroke is essential for timely prevention and cure. Various conventional statistical methods and computational intelligent models have been developed for predicting the risk and outcome of stroke. This research work focuses on a multilevel approach for predicting the occurrence of stroke based on various risk factors and invasive techniques like retinal imaging. This risk prediction model can aid in clinical decision making and help patients to have an improved and reliable risk prediction.

Keywords: prediction, retinal imaging, risk factors, stroke

Procedia PDF Downloads 270

Authors: Kassaye Balkew Workagegn, Gunnar Klemetsdal, Hans Magnus Gjøen

Abstract:

In this study, the first objective was to investigate whether non-lethal or non-invasive methods, utilizing body measurements, could be used to efficiently predict fillet weight and fillet yield for a complete diallel cross of three Nile tilapia (Oreochromis niloticus) strains collected from three Ethiopian Rift Valley lakes, Lakes Ziway, Koka and Chamo. The second objective was to estimate heritability of body weight, actual and predicted fillet traits, as well as genetic correlations between these traits. A third goal was to estimate additive, reciprocal, and heterosis effects for body weight and the various fillet traits. As in females, early sexual maturation was widespread, only 958 male fish from 81 full-sib families were used, both for the prediction of fillet traits and in genetic analysis. The prediction equations from body measurements were established by forward regression analysis, choosing models with the least predicted residual error sums of squares (PRESS). The results revealed that body measurements on live Nile tilapia is well suited to predict fillet weight but not fillet yield (R²= 0.945 and 0.209, respectively), but both models were seemingly unbiased. The genetic analyses were carried out with bivariate, multibreed models. Body weight, fillet weight, and predicted fillet weight were all estimated with a heritability ranged from 0.23 to 0.28, and with genetic correlations close to one. Contrary, fillet yield was only to a minor degree heritable (0.05), while predicted fillet yield obtained a heritability of 0.19, being a resultant of two body weight variables known to have high heritability. The latter trait was estimated with genetic correlations to body weight and fillet weight traits larger than 0.82. No significant differences among strains were found for their additive genetic, reciprocal, or heterosis effects, while total heterosis effects were estimated as positive and significant (P < 0.05). As a conclusion, prediction of prediction of fillet weight based on body measurements is possible, but not for fillet yield.

Keywords: additive, fillet traits, genetic correlation, heritability, heterosis, prediction, reciprocal

Procedia PDF Downloads 133

Authors: Krzysztof Pomorski

Abstract:

In the given work we present universal mathematical framework for modeling of cattle farm system that can set and validate various hypothesis that can be tested against experimental data. The presented work is preliminary but it is expected to be valid tool for future deeper analysis that can result in new class of prediction methods allowing early detection of cow dieseaes as well as cow performance. Therefore the presented work shall have its meaning in agriculture models and in machine learning as well. It also opens the possibilities for incorporation of certain class of biological models necessary in modeling of cow behavior and farm performance that might include the impact of environment on the farm system. Particular attention is paid to the model of coupled oscillators that it the basic building hypothesis that can construct the model showing certain periodic or quasiperiodic behavior.

Keywords: coupled ordinary differential equations, cattle farm system, numerical methods, stochastic differential equations

Procedia PDF Downloads 119

Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

Abstract:

Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

Procedia PDF Downloads 369

Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

Procedia PDF Downloads 243

Authors: Muhammad Awais Shafique, Eiji Hato, Hideki Yaginuma

Abstract:

Recently GPS data is used in a lot of studies to automatically reconstruct travel patterns for trip survey. The aim is to minimize the use of questionnaire surveys and travel diaries so as to reduce their negative effects. In this paper data acquired from GPS and accelerometer embedded in smart phones is utilized to predict the mode of transportation used by the phone carrier. For prediction, Support Vector Machine (SVM) and Adaptive boosting (AdaBoost) are employed. Moreover a unique method to improve the prediction results from these algorithms is also proposed. Results suggest that the prediction accuracy of AdaBoost after improvement is relatively better than the rest.

Keywords: accelerometer, AdaBoost, GPS, mode prediction, support vector machine

Procedia PDF Downloads 324

Authors: Melusi Khumalo, Anastacia Dlamini

Abstract:

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

Procedia PDF Downloads 340

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

Abstract:

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

Procedia PDF Downloads 266

Authors: Archit Yajnik, Rustam Ali

Abstract:

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

Procedia PDF Downloads 442

Authors: Carl van Walraven, Meltem Tuna

Abstract:

Background: Network meta-analysis (NMA) quantifies the relative efficacy of 3 or more interventions from studies containing a subgroup of interventions. This study applied the analytical approach of NMA to quantify the relative accuracy of prediction models with distinct inclusion criteria that are evaluated on a common population (‘concurrent external validation’). Methods: We simulated binary events in 5000 patients using a known risk function. We biased the risk function and modified its precision by pre-specified amounts to create 15 prediction models with varying accuracy and distinct patient applicability. Prediction model accuracy was measured using the Scaled Brier Score (SBS). Overall prediction model accuracy was measured using fixed-effects methods that accounted for model applicability patterns. Prediction model accuracy was summarized as the Network Relative Model Accuracy (NeRMA) Score which ranges from -∞ through 0 (accuracy of random guessing) to 1 (accuracy of most accurate model in concurrent external validation). Results: The unbiased prediction model had the highest SBS. The NeRMA score correctly ranked all simulated prediction models by the extent of bias from the known risk function. A SAS macro and R-function was created to implement the NeRMA Score. Conclusions: The NeRMA Score makes it possible to quantify the accuracy of binomial prediction models having distinct inclusion criteria in a concurrent external validation.

Keywords: prediction model accuracy, scaled brier score, fixed effects methods, concurrent external validation

Procedia PDF Downloads 180

Authors: Arvinder Kaur, Deepti Chopra

Abstract:

Software Entropy Metrics for bug prediction have been validated on various software systems by different researchers. In our previous research, we have validated that Software Entropy Metrics calculated for Mozilla subsystem’s predict the future bugs reasonably well. In this study, the Software Entropy metrics are calculated for a subsystem of Android and it is noticed that these metrics are not suitable for bug prediction. The results are compared with a subsystem of Mozilla and a comparison is made between the two software systems to determine the reasons why Software Entropy metrics are not applicable for Android.

Keywords: android, bug prediction, mining software repositories, software entropy

Procedia PDF Downloads 552

Authors: Amit R. Bhende, G. K. Awari

Abstract:

Remaining useful life (RUL) prediction is one of key technologies to realize prognostics and health management that is being widely applied in many industrial systems to ensure high system availability over their life cycles. The present work proposes a data-driven method of RUL prediction based on multiple health state assessment for rolling element bearings. Bearing degradation data at three different conditions from run to failure is used. A RUL prediction model is separately built in each condition. Feed forward back propagation neural network models are developed for prediction modeling.

Keywords: bearing degradation data, remaining useful life (RUL), back propagation, prognosis

Procedia PDF Downloads 408

Authors: Qiang Zhang, Chun Yuan

Abstract:

Since the PU (Prediction Unit) decision process is the most time consuming part of the emerging HEVC (High Efficient Video Coding) standardin intra and inter frame coding, this paper proposes the fast PU decision algorithm and speed up the algorithm using CUDA (Compute Unified Device Architecture). In intra frame coding, the fast PU decision algorithm uses the texture features to skip intra-frame prediction or terminal the intra-frame prediction for smaller PU size. In inter frame coding of HEVC, the fast PU decision algorithm takes use of the similarity of its own two Nx2N size PU's motion vectors and the hierarchical structure of CU (Coding Unit) partition to skip some modes of PU partition, so as to reduce the motion estimation times. The accelerate algorithm using CUDA is based on the fast PU decision algorithm which uses the GPU to make the motion search and the gradient computation could be parallel computed. The proposed algorithm achieves up to 57% time saving compared to the HM 10.0 with little rate-distortion losses (0.043dB drop and 1.82% bitrate increase on average).

Keywords: HEVC, PU decision, inter prediction, intra prediction, CUDA, parallel

Procedia PDF Downloads 370

Authors: J. K. Alhassan, C. S. Actsu

Abstract:

This study is on the prediction of feature performance of undergraduate students with Artificial Neural Networks (ANN). With the growing decline in the quality academic performance of undergraduate students, it has become essential to predict the students’ feature academic performance early in their courses of first and second years and to take the necessary precautions using such prediction-based information. The feed forward multilayer neural network model was used to train and develop a network and the test carried out with some of the input variables. A result of 80% accuracy was obtained from the test which was carried out, with an average error of 0.009781.

Keywords: academic performance, artificial neural network, prediction, students

Procedia PDF Downloads 429

Authors: Mohammad Ghavami, Reza S. Dilmaghani

Abstract:

This paper presents an adaptive framework for modelling financial markets using equity risk premiums, risk free rates and volatilities. The recorded economic factors are initially used to train four adaptive filters for a certain limited period of time in the past. Once the systems are trained, the adjusted coefficients are used for modelling and prediction of an important financial market index. Two different approaches based on least mean squares (LMS) and recursive least squares (RLS) algorithms are investigated. Performance analysis of each method in terms of the mean squared error (MSE) is presented and the results are discussed. Computer simulations carried out using recorded data show MSEs of 4% and 3.4% for the next month prediction using LMS and RLS adaptive algorithms, respectively. In terms of twelve months prediction, RLS method shows a better tendency estimation compared to the LMS algorithm.

Keywords: adaptive methods, LSE, MSE, prediction of financial Markets

Procedia PDF Downloads 302

Authors: Seyoung Kim, Jeongmin Kim, Kwang Ryel Ryu

Abstract:

A database that records average traffic speeds measured at five-minute intervals for all the links in the traffic network of a metropolitan city. While learning from this data the models that can predict future traffic speed would be beneficial for the applications such as the car navigation system, building predictive models for every link becomes a nontrivial job if the number of links in a given network is huge. An advantage of adopting k-nearest neighbor (k-NN) as predictive models is that it does not require any explicit model building. Instead, k-NN takes a long time to make a prediction because it needs to search for the k-nearest neighbors in the database at prediction time. In this paper, we investigate how much we can speed up k-NN in making traffic speed predictions by reducing the amount of data to be searched for without a significant sacrifice of prediction accuracy. The rationale behind this is that we had a better look at only the recent data because the traffic patterns not only repeat daily or weekly but also change over time. In our experiments, we build several different k-NN models employing different sets of features which are the current and past traffic speeds of the target link and the neighbor links in its up/down-stream. The performances of these models are compared by measuring the average prediction accuracy and the average time taken to make a prediction using various amounts of data.

Keywords: big data, k-NN, machine learning, traffic speed prediction

Procedia PDF Downloads 329

Authors: Minas Balyan

Abstract:

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

Procedia PDF Downloads 358

Authors: Jiun Jeon, Byung-Ju Yi

Abstract:

This paper investigates modeling and shape prediction of elastic kinematic chains such as colonoscopy. 2D and 3D models of elastic kinematic chains are suggested and their behaviors are demonstrated through simulation. To corroborate the effectiveness of those models, experimental work is performed using a magnetic sensor system.

Keywords: elastic kinematic chain, shape prediction, colonoscopy, modeling

Procedia PDF Downloads 565

Authors: Li Yu, Chenlu Jiao, Hongrun Xin, Yan Wang, Kaiyang Wang

Abstract:

In order to study the impact of various factors on the housing price, we propose to build different prediction models based on deep learning to determine the existing data of the real estate in order to more accurately predict the housing price or its changing trend in the future. Considering that the factors which affect the housing price vary widely, the proposed prediction models include two categories. The first one is based on multiple characteristic factors of the real estate. We built Convolution Neural Network (CNN) prediction model and Long Short-Term Memory (LSTM) neural network prediction model based on deep learning, and logical regression model was implemented to make a comparison between these three models. Another prediction model is time series model. Based on deep learning, we proposed an LSTM-1 model purely regard to time series, then implementing and comparing the LSTM model and the Auto-Regressive and Moving Average (ARMA) model. In this paper, comprehensive study of the second-hand housing price in Beijing has been conducted from three aspects: crawling and analyzing, housing price predicting, and the result comparing. Ultimately the best model program was produced, which is of great significance to evaluation and prediction of the housing price in the real estate industry.

Keywords: deep learning, convolutional neural network, LSTM, housing prediction

Procedia PDF Downloads 275

Authors: Farid Nouioua, Abdelouaheb Ardjouni

Abstract:

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

Procedia PDF Downloads 404

Authors: Waqas Ahmed Khan Afridi, Subhas Chandra Mukhopadhyay, Bandita Mainali

Abstract:

The research paper presents a unique approach to evapotranspiration (ET) prediction using a Support Vector Machine (SVM) learning algorithm. The study leverages real-time sensor node data to develop an accurate and adaptable prediction model, addressing the inherent challenges of traditional ET estimation methods. The integration of the SVM algorithm with real-time sensor node data offers great potential to improve spatial and temporal resolution in ET predictions. In the model development, key input features are measured and computed using mathematical equations such as Penman-Monteith (FAO56) and soil water balance (SWB), which include soil-environmental parameters such as; solar radiation (Rs), air temperature (T), atmospheric pressure (P), relative humidity (RH), wind speed (u2), rain (R), deep percolation (DP), soil temperature (ST), and change in soil moisture (∆SM). The one-year field data are split into combinations of three proportions i.e. train, test, and validation sets. While kernel functions with tuning hyperparameters have been used to train and improve the accuracy of the prediction model with multiple iterations. This paper also outlines the existing methods and the machine learning techniques to determine Evapotranspiration, data collection and preprocessing, model construction, and evaluation metrics, highlighting the significance of SVM in advancing the field of ET prediction. The results demonstrate the robustness and high predictability of the developed model on the basis of performance evaluation metrics (R2, RMSE, MAE). The effectiveness of the proposed model in capturing complex relationships within soil and environmental parameters provide insights into its potential applications for water resource management and hydrological ecosystem.

Keywords: evapotranspiration, FAO56, KNIME, machine learning, RStudio, SVM, sensors

Procedia PDF Downloads 33

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

Abstract:

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

Procedia PDF Downloads 55

Authors: Zuhier Altawallbeh

Abstract:

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

Procedia PDF Downloads 396

Authors: Mustafa Ekici

Abstract:

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

Procedia PDF Downloads 434

Authors: Meziane Belkacem

Abstract:

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

Procedia PDF Downloads 126