LAPLACE DECOMPOSITION METHOD FOR SOLVING FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS WITH INITIAL VALUE PROBLEMS

Fredholm integro-differential equations (IDEs) are important mathematical models used in various scientific disciplines. However, the presence of nonlinearity in these equations poses significant challenges for conventional numerical methods like quadrature formulas. This paper explores the application of the Laplace decomposition method (LDM) to address this problem. By employing the LDM and the Adomian decomposition method (ADM), the nonlinear Fredholm integro-differential equations with initial value problems were transformed into a sequence of solvable nonlinear integral equations. LDM is the semi-analytical technique specifically designed for nonlinear IDEs, offered an efficient approximation approach. The study presented the results of solving four illustrative examples using LDM and conducted a comparative analysis with other methods such as ADM and homotopy perturbation Method (HPM). The results demonstrated that LDM achieved exceptional accuracy and efficiency for nonlinear Fredholm IDEs.