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On the decomposition method for system of linear equations and system of linear Volterra integral equations. (English) Zbl 1032.65027
Summary: We 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, the so-called Picard’s method, is discussed. Finally, numerical examples are prepared to illustrate these considerations.
MSC:
65F10Iterative methods for linear systems
45F05Systems of nonsingular linear integral equations
65R20Integral equations (numerical methods)