The numerical method for solving Volterra–Fredholm integro-differential equations of the second kind based on the meshless method

Abstract

This paper explains a numerical scheme based on the moving least squares (MLS) method to solve Volterra-Fredholm integro-differential equations in one-dimensional space. The method is a meshless method, since it does not need any background interpolation or approximation cells, so it does not depend on the geometry of domain. The demand of meshless techniques increases because of its meshless nature and simplicity of usage in higher dimensions. We show the convergence analysis for this technique to stress its reliability, and eventually some examples are presented to indicate the applicability of the method. The approximate results of this technique are compared with the correct solutions, which reveals that this technique meets with the approval of the correct solutions to the problems.