Proposing Modified Successive Approximation Method for Treating Two Dimensional Volterra Integral Equations

Abstract

     The primary goal of this study is to investigate and enhance the successive approximation method (SAM) for addressing two dimensional Volterra integral equation of the second kind (TDVIE-2). By comparing numerical solutions with exact solutions, the aim is to achieve improved efficiency and simplicity. These iterative techniques are underpinned by several novel theorems concerning convergence, stability, and robustness. The newly proposed method is supported by favorable simulation outcomes and examples drawn from various case studies utilizing Matlab software.