A Numerical Algorithm for Solving Nonlinear Delay Volterra Integral Equations by Means of Homotopy Perturbation Method

2011 ◽  
Vol 12 (1-8) ◽  
Author(s):  
Solat Karimi Vanani ◽  
Ahmet Yıldırım ◽  
F. Soleymani ◽  
M. Khan
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Numerical Algorithm ◽  
Homotopy Perturbation Method ◽  
Volterra Integral Equations ◽  
Homotopy Perturbation ◽  
Nonlinear Delay

scholarly journals Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1730 ◽  
Author(s):  
Samad Noeiaghdam ◽  
Aliona Dreglea ◽  
Jihuan He ◽  
Zakieh Avazzadeh ◽  
Muhammad Suleman ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Error Estimation ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Energy System ◽  
Volterra Integral Equations ◽  
Stochastic Arithmetic ◽  
Homotopy Perturbation ◽  
Cadna Library

This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method.

scholarly journals MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING INTEGRAL EQUATIONS

2010 ◽  
Vol 24 (24) ◽  
pp. 4741-4746 ◽  
Author(s):  
JAFAR SABERI-NADJAFI ◽  
MOHAMADREZA TAMAMGAR
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
Volterra Integral Equations ◽  
Homotopy Perturbation

This paper proposes a modified homotopy perturbation method to solve Fredholm and Volterra integral equations. Comparison of the obtained results with those obtained by the standard homotopy perturbation method shows that the proposed method is very effective and simple.

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