COMPARATIVE ANALYSIS OF VIA AND SEM METHODS FOR SOLVING FREDHOLM LINEAR INTEGRO-DIFFERENTIAL EQUATIONS

Abstract

This study presents a comparative analysis of the Variational Iteration Method (VIM) and the Series Expansion Method (SEM) for solving Fredholm Integro-Differential Equations (FIDEs). Both methods were applied to an illustrative example, showcasing their effectiveness in addressing this class of equations. While SEM provided approximate solutions with acceptable accuracy, VIM demonstrated a distinct advantage by delivering exact solutions. The performance of the methods was evaluated through numerical experiments, with results presented using graphs and tables for clarity. SEM, though straightforward in its approach, exhibited slower convergence and reduced precision. On the other hand, VIM, employing correction functionals and Lagrange multipliers, consistently achieved high accuracy with minimal computational effort. The findings confirm that while both methods are effective, VIM is the more reliable and efficient approach for solving FIDEs. Its ability to produce exact solutions highlights its suitability for practical applications in mathematics and engineering.