An Iterative Approach to Solve Volterra Nonlinear Integral Equations (European Journal of Pure and Applied Mathematics, 2023)
In this study, we provide the Aboodh decomposition method, a novel analytical technique. The fundamental definitions and theorems of the suggested approach are provided and analyzed. This new method is a novel mixture of the Aboodh transform and the Adomian decomposition method. The new method is used to solve nonlinear integro-differential equations (IDEs), and the solutions are given as quickly expanding series of terms. We compute the maximum absolute error and provide some figures to compare the resulting approximative solutions with the exact ones in order to demonstrate the method’s applicability and efficiency.
Keywords: Aboodh transform; Decomposition method; Integral equations; Nonlinear integro-differential equations