a comparison between the homotopy perturbation method and adomian’s decomposition method for solving nonlinear volterra integral equations

A comparison between the Homotopy Perturbation Method and Adomian’s Decomposition Method for Solving Nonlinear Volterra Integral Equations

In this paper, we conduct a comparative study between the homotopy perturbation method (HPM) and Adomian’s decomposition method (ADM) for analytic treatment of nonlinear Volterra integral equations, and we show that the HPM with a specific convex homotopy is equivalent to the ADM for these type of equations.

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

T-Stability Approach to the Homotopy Perturbation Method for Solving Fredholm Integral Equations

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...

A computational method for nonlinear mixed Volterra-Fredholm integral equations

In this article the nonlinear mixed Volterra-Fredholm integral equations are investigated by means of the modied three-dimensional block-pulse functions (M3D-BFs). This method converts the nonlinear mixed Volterra-Fredholm integral equations into a nonlinear system of algebraic equations. The illustrative   examples are provided to demonstrate the applicability and simplicity of our   scheme.    

Modified homotopy perturbation method for solving non-linear oscillator's ‎equations

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...

A Method for Solving Nonlinear Volterra Integral Equations

It is known that to construct the stable multistep method with the higher order of accuracy for solving integral equation is actual. For this aim here we suggest some ways for the construction of hybrid methods for solving nonlinear Volterra integral equations of the second kind. Thus, foundational this extends stable hybrid method with higher order of accuracy. Note that the hybrid methods whi...