A Novel Approach to Solve Nonlinear Higher Order VFIDE Using the Laplace Transform and Adomian Decomposition Method

This study explores the application of a novel approach called theLaplace Discrete ModifiedAdomian Decomposition Method(LDMADM) to solve non-homogeneous higher-order nonlinearVFIDEs. LDMADM is an extension of theLaplace Modified Adomian Decomposition Method(LMADM)and combines it with quadrature integration criteria to improve accuracy. The proposed method isevaluated by comparing its results with exact solutions and calculating absolute error measurements.The study establishes the existence of unique solutions and presents experimental, numerical findingsthat demonstrate the high accuracy and effectiveness of the LDMADM approach. This method offersa promising alternative to analytical approaches for solving higher-order nonlinearVolterra Fredholm-type Integro Differential Equations(VFIDEs).