Numerical solutions of the nonlinear integro-differential equations: Wavelet-Galerkin method and homotopy perturbation method

2007 ◽  
Vol 188 (1) ◽  
pp. 450-455 ◽  
Author(s):  
M. Ghasemi ◽  
M. Tavassoli kajani ◽  
E. Babolian
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Galerkin Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Homotopy Perturbation ◽  
Wavelet Galerkin Method

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

scholarly journals On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
E. E. Eladdad ◽  
E. A. Tarif
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In the current work, a combination between a new integral transform and the homotopy perturbation method is presented. This combination allows to obtain analytic and numerical solutions for linear and nonlinear systems of partial differential equations.

scholarly journals Numerical Solutions of Fourth-Order Fractional Integro-Differential Equations

2010 ◽  
Vol 65 (12) ◽  
pp. 1027-1032 ◽  
Author(s):  
Ahmet Yıldırım ◽  
Sefa Anıl Sezer ◽  
Yasemin Kaplan
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fourth Order ◽  
Fractional Derivatives ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Methods Numerical

In this paper, the homotopy perturbation method (HPM) is developed to obtain numerical solutions of linear and nonlinear boundary value problems for fourth-order fractional integro-differential equations. The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy perturbation method is very effective and convenient and overcome the difficulty of traditional methods. Numerical examples are presented to illustrate the efficiency, simplicity, and reliability of the method.

scholarly journals Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 40 ◽  
Author(s):  
Shumaila Javeed ◽  
Dumitru Baleanu ◽  
Asif Waheed ◽  
Mansoor Shaukat Khan ◽  
Hira Affan
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Order Differential Equations ◽  
Homotopy Perturbation ◽  
The Given ◽  
Ordinary Derivative

The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for α = 1 , is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.

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