Approximate solution to solve non-linear integro-differential type defined using boundary value problems

Abstract

In this paper, we analyze a boundary value problem (BVP) for a nonlinear integro-Volterra-Fredholm integral equation with variable coefficients. We employ common numerical methods such as the homotopy analysis technique developed by Liao and the modified Adomain decomposition technique to construct an approximate numerical solution. Graphical representations show that these methods are the most efficient and convenient. Additionally, we examine the conditions that guarantee the existence and distinctiveness of the solution for different types of kernels and levels of non-linearity. We provide numerical examples to demonstrate the applicability of our main theorems, and to determine the convergence and accuracy of our proposed technique.