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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:

65F10 Iterative numerical methods for linear systems
45F05 Systems of nonsingular linear integral equations
65R20 Numerical methods for integral equations
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References:

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