Search results for: grey clustering method

Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

Procedia PDF Downloads 523

Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Amhimmid Mohammed Saffour, Abdelkader Salama

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Filtering is a part of image enhancement techniques, it is used to enhance certain details such as edges in the image that are relevant to the application. Additionally, filtering can even be used to eliminate unwanted components of noise. Medical images typically contain salt and pepper noise and Poisson noise. This noise appears to the presence of minute grey scale variations within the image. In this paper, different filters techniques namely (Median, Wiener, Rank order3, Rank order5, and Average) were applied on CT medical images (Brain and chest). We using all these filters to remove salt and pepper noise from these images. This type of noise consists of random pixels being set to black or white. Peak Signal to Noise Ratio (PSNR), Mean Square Error r(MSE) and Histogram were used to evaluated the quality of filtered images. The results, which we have achieved shows that, these filters, are more useful and they prove to be helpful for general medical practitioners to analyze the symptoms of the patients with no difficulty.

Keywords: CT imaging, median filter, adaptive filter and average filter, MATLAB

Procedia PDF Downloads 301

Authors: Dina Ahmed Selim, Eman Shawky Anwar, Rasha Mohamed Abu El-Khair

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A rapid, simple and efficient method with minimal sample treatment was developed for authentication of Garcinia cambogia fruit peel powder, along with determining undeclared active pharmaceutical ingredients (APIs) in its herbal slimming dietary supplements using near infrared spectroscopy combined with chemometrics. Five featured adulterants, including sibutramine, metformin, orlistat, ephedrine, and theophylline are selected as target compounds. The Near infrared spectral data matrix of authentic Garcinia cambogia fruit peel and specimens degraded by intentional contamination with the five selected APIs was subjected to hierarchical clustering analysis to investigate their bundling figure. SIMCA models were established to ensure the genuiness of Garcinia cambogia fruit peel which resulted in perfect classification of all tested specimens. Adulterated samples were utilized for construction of PLSR models based on different APIs contents at minute levels of fraud practices (LOQ < 0.2% w/w).The suggested approach can be applied to enhance and guarantee the safety and quality of Garcinia fruit peel powder as raw material and in dietary supplements.

Keywords: Garcinia cambogia, Quality control, NIR spectroscopy, Chemometrics

Procedia PDF Downloads 65

Authors: Denver E. Severt, Cynthia Mejia

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With a grey wave sweeping across the world and people living longer than ever, more individuals will reside in retirement communities in unprecedented numbers. Enhancing the resident stay within these communities is imperative to reduce past stigmas associated with senior communities. This exploratory quantitative investigation examined interview contents of employees and residents to see if empathy was observed. The results showed the employees across all ranges had a much better grasp of affective empathy, yet with greater experience and age, it was clear that cognitive empathy had to be used with affective empathy in order to gain better trust across the community of residents. Outcomes from the study suggest that future training programs for employees are operationalized to include both affective and cognitive empathy practices. This study is unique in that two scales of empathy were transformed into qualitative questions, and in-depth employee and resident interviews were conducted. The study answers many calls of research to provide more specific studies in senior living communities.

Keywords: senior living community, transformational service research, qualitative research

Procedia PDF Downloads 121

Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

Procedia PDF Downloads 394

Authors: Alkaben Patel

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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

Procedia PDF Downloads 312

Authors: Cesar Hernández, Diego Giral, Ingrid Páez

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This article proposes a hybrid algorithm for spectrum allocation in cognitive radio networks based on the algorithms Analytical Hierarchical Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to improve the performance of the spectrum mobility of secondary users in cognitive radio networks. To calculate the level of performance of the proposed algorithm a comparative analysis between the proposed AHP-TOPSIS, Grey Relational Analysis (GRA) and Multiplicative Exponent Weighting (MEW) algorithm is performed. Four evaluation metrics is used. These metrics are the accumulative average of failed handoffs, the accumulative average of handoffs performed, the accumulative average of transmission bandwidth, and the accumulative average of the transmission delay. The results of the comparison show that AHP-TOPSIS Algorithm provides 2.4 times better performance compared to a GRA Algorithm and, 1.5 times better than the MEW Algorithm.

Keywords: cognitive radio, decision making, hybrid algorithm, spectrum handoff, wireless networks

Procedia PDF Downloads 520

Authors: Igor Filikhin, Vladimir M. Suslov, Roman Ya. Kezerashvili, Branislav Vlahivic

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The mass-polarization term of the three-body kinetic energy operator is evaluated for different systems which include two identical particles: A+A+B. The term has to be taken into account for the analysis of AB- and AA-interactions based on experimental data for two- and three-body ground state energies. In this study, we present three-body calculations within the framework of a potential model for the kaonic clusters K−K−p and ppK−, nucleus 3H and hypernucleus 6 ΛΛHe. The systems are well clustering as A+ (A+B) with a ground state energy E2 for the pair A+B. The calculations are performed using the method of the Faddeev equations in configuration space. The phenomenological pair potentials were used. We show a correlation between the mass ratio mA/mB and the value δB of the mass-polarization term. For bosonic-like systems, this value is defined as δB = 2E2 − E3, where E3 is three-body energy when VAA = 0. For the systems including three particles with spin(isospin), the models with average AB-potentials are used. In this case, the Faddeev equations become a scalar one like for the bosonic-like system αΛΛ. We show that the additional energy conected with the mass-polarization term can be decomposite to a sum of the two parts: exchenge related and reduced mass related. The state of the system can be described as the following: the particle A1 is bound within the A + B pair with the energy E2, and the second particle A2 is bound with the pair with the energy E3 − E2. Due to the identity of A particles, the particles A1 and A2 are interchangeable in the pair A + B. We shown that the mass polarization δB correlates with a type of AB potential using the system αΛΛ as an example.

Keywords: three-body systems, mass polarization, Faddeev equations, nuclear interactions

Procedia PDF Downloads 349

Authors: Daniela V. Bavaresco, Tamy Colonetti, Antonio Jose Grande, Francesc Colom, Joao Quevedo, Samira S. Valvassori, Maria Ines da Rosa

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Objective: Performed a systematic review and meta-analysis to evaluated the potential effect of the cyclo-oxygenases (Cox)-2 inhibitor Celecoxib adjunct treatment in Bipolar Disorder (BD), through of randomized controlled trials. Method: A search of the electronic databases was proceeded, on MEDLINE, EMBASE, Scopus, Cochrane Central Register of Controlled Trials (CENTRAL), Biomed Central, Web of Science, IBECS, LILACS, PsycINFO (American Psychological Association), Congress Abstracts, and Grey literature (Google Scholar and the British Library) for studies published from January 1990 to February 2018. A search strategy was developed using the terms: 'Bipolar disorder' or 'Bipolar mania' or 'Bipolar depression' or 'Bipolar mixed' or 'Bipolar euthymic' and 'Celecoxib' or 'Cyclooxygenase-2 inhibitors' or 'Cox-2 inhibitors' as text words and Medical Subject Headings (i.e., MeSH and EMTREE) and searched. The therapeutic effects of adjunctive treatment with Celecoxib were analyzed, it was possible to carry out a meta-analysis of three studies included in the systematic review. The meta-analysis was performed including the final results of the Young Mania Rating Scale (YMRS) at the end of randomized controlled trials (RCT). Results: Three primary studies were included in the systematic review, with a total of 121 patients. The meta-analysis had significant effect in the YMRS scores from patients with BD who used Celecoxib adjuvant treatment in comparison to placebo. The weighted mean difference was 5.54 (95%CI=3.26-7.82); p < 0.001; I2 =0%). Conclusion: The systematic review suggests that adjuvant treatment with Celecoxib improves the response of major treatments in patients with BD when compared with adjuvant placebo treatment.

Keywords: bipolar disorder, Cox-2 inhibitors, Celecoxib, systematic review, meta-analysis

Procedia PDF Downloads 473

Authors: Fei Gao, Xinyang Dong, Yisu Ge, Shufang Lu, Libo Weng

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Vehicle color recognition plays an important role in traffic accident investigation. However, due to the influence of illumination, weather, and noise, vehicle color recognition still faces challenges. In this paper, a vehicle color classification network based on spatial cluster loss and channel attention mechanism (SCNet) is proposed for vehicle color recognition. A channel attention module is applied to extract the features of vehicle color representative regions and reduce the weight of nonrepresentative color regions in the channel. The proposed loss function, called spatial clustering loss (SC-loss), consists of two channel-specific components, such as a concentration component and a diversity component. The concentration component forces all feature channels belonging to the same class to be concentrated through the channel cluster. The diversity components impose additional constraints on the channels through the mean distance coefficient, making them mutually exclusive in spatial dimensions. In the comparison experiments, the proposed method can achieve state-of-the-art performance on the public datasets, VCD, and VeRi, which are 96.1% and 96.2%, respectively. In addition, the ablation experiment further proves that SC-loss can effectively improve the accuracy of vehicle color recognition.

Keywords: feature extraction, convolutional neural networks, intelligent transportation, vehicle color recognition

Procedia PDF Downloads 156

Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

Procedia PDF Downloads 286

Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Waleed Sulaiman Shingaly

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The Ordivician-Khabour Formation from the Northern Thrust Zone of Iraqi-Kurdistan comprises between 500 and 800 m of alternating predominantly greenish-grey sandstones, siltstones and shales. The succession has revealed an abundant ichnofossils characterized by 11 ichnogenus, namely: Helminthopsis, Gordia, Cruziana, Rusophycus, Monomorphichnus, Rhizocorallium, Thalassinoide, Planolite, Paleophycus, Deplocraterion and Skolithose. Ethologically these ichnogenera display dwelling and feeding activities of the infaunal organisms. This association of ichnofossils contains elements of the Skolithose and Cruziana ichnofacies. The presence of Skolithos ichnofacies indicates sandy shifting substrate and high energy conditions in foreshore zone while the Cruziana ichnofacies indicate unconsolidated, poorly sorted soft substrate and low energy condition in the shore face/offshore zone. These ichnogenera indicate shoreface-offshore zone of shallow-marine environment for the deposition of the rocks of the Khabour Formation.

Keywords: Ichnofossils, shoreface-offshore zone, Khabour Formation, Iraq

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

Procedia PDF Downloads 577

Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

Procedia PDF Downloads 373

Authors: Xinke Huang, Huan Wang, Lidong Guo, Changbin Ju, Runbiao Liu, Guoen Cao, Yibo Wang, Honghua Xu

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Grid connected photovoltaic (PV) power system is to be developed in the direction of large-scale, clustering. Large-scale PV generation systems connected to HVDC grid have many advantages compared to its counterpart of AC grid, and DC connection is the tendency. DC/DC converter as the most important device in the system, has become one of the hot spots recently. The paper proposes a Quasi Z-Source(QZS) based Boost Full Bridge Isolated DC/DC Converter(BFBIC) topology as a basis power module and combination through input parallel output series(IPOS) method to improve power capacity and output voltage to match with the HVDC grid. The topology has both traditional voltage source and current source advantages, it permit the H-bridge short through and open circuit, which adopt utility duty cycle control and achieved input current and output voltage balancing through input current sharing control strategy. A ±10kV/200kW system model is built in MATLAB/SIMULINK to verify the proposed topology and control strategy.

Keywords: PV Generation System, Cascaded DC/DC converter, HVDC, Quasi Z Source Converter

Procedia PDF Downloads 373

Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

Procedia PDF Downloads 239

Authors: Guettal Djaouida, Ziadi Abdelkader

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In this paper, we study a coupling of the Alienor method with the algorithm of Piyavskii-Shubert. The classical multidimensional global optimization methods involves great difficulties for their implementation to high dimensions. The Alienor method allows to transform a multivariable function into a function of a single variable for which it is possible to use efficient and rapid method for calculating the the global optimum. This simplification is based on the using of a reducing transformation called Alienor.

Keywords: global optimization, reducing transformation, α-dense curves, Alienor method, Piyavskii-Shubert algorithm

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

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The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: exponential smoothing method, open data, operation estimation, train schedule

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Authors: Maryam Khazaei Pool, Lori Lewis

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This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method, Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions, including Burgers equation, spline functions, and B-spline functions, are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided, and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ equation, Septic B-spline, modified cubic B-spline differential quadrature method, exponential cubic B-spline technique, B-spline Galerkin method, quintic B-spline Galerkin method

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Authors: Juan F. P. Ramírez, Jésica A. L. Isaza, Benjamín A. Rojano

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This study proposes a novel use of a method to determine the mechanical properties of fruits by the use of the indentation tests. The method combines experimental results with a numerical finite elements model. The results presented correspond to a simplified numerical modeling of banana. The banana was assumed as one-layer material with an isotropic linear elastic mechanical behavior, the Young’s modulus found is 0.3Mpa. The method will be extended to multilayer models in further studies.

Keywords: finite element method, fruits, inverse analysis, mechanical properties

Procedia PDF Downloads 339

Authors: Amara Prakasa Rao, N. V. S. N. Sarma

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This paper describes the synthesis of linear array geometry with minimum sidelobe level and null control using the Taguchi method. Based on the concept of the orthogonal array, Taguchi method effectively reduces the number of tests required in an optimization process. Taguchi method has been successfully applied in many fields such as mechanical, chemical engineering, power electronics, etc. Compared to other evolutionary methods such as genetic algorithms, simulated annealing and particle swarm optimization, the Taguchi method is much easier to understand and implement. It requires less computational/iteration processing to optimize the problem. Different cases are considered to illustrate the performance of this technique. Simulation results show that this method outperforms the other evolution algorithms (like GA, PSO) for smart antenna systems design.

Keywords: array factor, beamforming, null placement, optimization method, orthogonal array, Taguchi method, smart antenna system

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Authors: Shahabeddin Sotudian, M. H. Fazel Zarandi, I. B. Turksen

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Hepatitis is one of the most common and dangerous diseases that affects humankind, and exposes millions of people to serious health risks every year. Diagnosis of Hepatitis has always been a challenge for physicians. This paper presents an effective method for diagnosis of hepatitis based on interval Type-II fuzzy. This proposed system includes three steps: pre-processing (feature selection), Type-I and Type-II fuzzy classification, and system evaluation. KNN-FD feature selection is used as the preprocessing step in order to exclude irrelevant features and to improve classification performance and efficiency in generating the classification model. In the fuzzy classification step, an “indirect approach” is used for fuzzy system modeling by implementing the exponential compactness and separation index for determining the number of rules in the fuzzy clustering approach. Therefore, we first proposed a Type-I fuzzy system that had an accuracy of approximately 90.9%. In the proposed system, the process of diagnosis faces vagueness and uncertainty in the final decision. Thus, the imprecise knowledge was managed by using interval Type-II fuzzy logic. The results that were obtained show that interval Type-II fuzzy has the ability to diagnose hepatitis with an average accuracy of 93.94%. The classification accuracy obtained is the highest one reached thus far. The aforementioned rate of accuracy demonstrates that the Type-II fuzzy system has a better performance in comparison to Type-I and indicates a higher capability of Type-II fuzzy system for modeling uncertainty.

Keywords: hepatitis disease, medical diagnosis, type-I fuzzy logic, type-II fuzzy logic, feature selection

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Authors: Ahd Aljarf, Saad Amin

Abstract:

Images are important source of information used as evidence during any investigation process. Their clarity and accuracy is essential and of the utmost importance for any investigation. Images are vulnerable to losing blocks and having noise added to them either after alteration or when the image was taken initially, therefore, having a high performance image processing system and it is implementation is very important in a forensic point of view. This paper focuses on improving the quality of the forensic images. For different reasons packets that store data can be affected, harmed or even lost because of noise. For example, sending the image through a wireless channel can cause loss of bits. These types of errors might give difficulties generally for the visual display quality of the forensic images. Two of the images problems: noise and losing blocks are covered. However, information which gets transmitted through any way of communication may suffer alteration from its original state or even lose important data due to the channel noise. Therefore, a developed system is introduced to improve the quality and clarity of the forensic images.

Keywords: image filtering, image reconstruction, image processing, forensic images

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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

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Authors: Sunyoung Bu, Wonkyu Chung, Philsu Kim

Abstract:

In this paper, we introduce a method for improving the embedded Runge-Kutta-Fehlberg 4(5) method. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. This solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, EULR problem is numerically solved.

Keywords: embedded Runge-Kutta-Fehlberg method, initial value problem, EULR problem, integration step

Procedia PDF Downloads 450