Adomian decomposition method for two-dimensional nonlinear volterra integral equations of the second kind

Abstract

Some methods based on the decomposition technique are presented for solving a class of nonlinear integral equations, the two-dimensional nonlinear Volterra integral equations of the second kind (VESK). Two algorithms of the Adomian decomposition method (ADM) and the Modified Adomian decomposition method (MADM) are implemented to solve the problems. The implementation of standard ADM may produce the exact solution while the MADM is used to obtain the numerical approximation of the VESK. From the analysis of convergence for numerical results, it is shown that four terms of the series solution provide a good approximation to the exact solution. Therefore, the ADM and MADM are shown to be effective and reliable for solving two-dimensional nonlinear VESK.