A Novel Approach to Solve Nonlinear Higher Order VFIDE Using the Laplace Transform and Adomian Decomposition Method - Miah, Bapan Ali; Sen, Mausumi; Gupta, Damini (Communications in Mathematics and Applications, 2024)
This study explores the application of a novel approach called the Laplace Discrete Modified Adomian Decomposition Method (LDMADM) to solve non-homogeneous higher-order nonlinear VFIDEs. LDMADM is an extension of the Laplace Modified Adomian Decomposition Method (LMADM) and combines it with quadrature integration criteria to improve accuracy. The proposed method is evaluated by comparing its results with exact solutions and calculating absolute error measurements. The study establishes the existence of unique solutions and presents experimental, numerical findings that demonstrate the high accuracy and effectiveness of the LDMADM approach. This method offers a promising alternative to analytical approaches for solving higher-order nonlinear Volterra Fredholmtype Integro Differential Equations (VFIDEs).