An Enhanced Temimi-Ansari Method for Solving Nonlinear Fredholm Integro-Differential Equations

Abstract

This study presents an enhanced version of the Temimi-Ansari Method (TAM) for effectively solving nonlinear integro-differential equations involving Fredholm-type integrals. The improved method builds upon the original TAM framework and demonstrates its robustness in addressing complex functional equations. Symbolic computation tools are employed to implement the method, and its performance is illustrated through several benchmark problems. The obtained results are compared with exact solutions and other semi-analytical techniques to validate the accuracy and efficiency of the proposed approach. The method proves to be computationally efficient, capable of simplifying calculations, and suitable for solving both linear and nonlinear Fredholm integro-differential equations of the second kind.