On the decomposition method for system of linear equations and system of linear Volterra integral equations

Abstract

In this paper, we will study the application of the Adomian decomposition method for two different classes of systems: The system of linear equations and the system of linear Volterra integral equations. For a system of linear equations we show that the Adomian decomposition method is equivalent to the classical Jacobi iterative method. Then the equivalence of the Adomian decomposition method for a system of linear Volterra integral equations and the successive approximations method, so called Picard’s method, are discussed. Finally, numerical examples are prepared to illustrate these considerations.