Numerical Comparison for Solution of Fredholm Integro-Differential Equations

Abstract

This study explores four prominent methods for solving integral and integro-differential equations: the Homotopy Perturbation Method, the Modified Adomian Decomposition Method, the Variational Iteration Method, and the Adomian Decomposition Method. While each approach has been widely used, a clear understanding of their comparative strengths remains underexplored, particularly for problems with known exact solutions. To address this gap, the study applies these methods to Fredholm's integro-differential equations and evaluates their accuracy. Results show that all methods yield successful approximate solutions, with differences in performance highlighted. These findings provide valuable insights into method selection for solving similar equations, advancing numerical analysis in applied mathematics.