Abstract
In this work, the main concept of the homotopy perturbation method (HPM) was outlined and convergence theorems of the HPM for solving some classes of nonlinear integral, integro-differential and differential equations were proved. A theorem for estimating the error in the approximate solution was proved as well. The proposed HPM convergence theorems were confirmed and the efficiency of the technique was explored by applying the HPM for solving several classes of nonlinear integral/integro-differential equations.
Highlights
The objective of this work was to further apply the homotopy perturbation method (HPM) [10,11,12,13,14,15,16] to some useful nonlinear integral/integro-differential models that arise in real-life applications
Before proceeding to prove a convergence theorem of the method to the nonlinear integral equations, we proposed a new formulation for the HPM to simplify proving the convergence theorem
We considered the fourth-order nonlinear integro-differential equation (NIDE) [29]: 0.3
Summary
The main concept of the homotopy perturbation method (HPM) was outlined and convergence theorems of the HPM for solving some classes of nonlinear integral, integrodifferential and differential equations were proved. A theorem for estimating the error in the approximate solution was proved as well. The proposed HPM convergence theorems were confirmed and the efficiency of the technique was explored by applying the HPM for solving several classes of nonlinear integral/integro-differential equations
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