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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:

[1] Adomian, G., Nonlinear Stochastic Systems Theory and Applications to Physics (1989), Kluwer: Kluwer Dordrecht · Zbl 0659.93003
[2] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer: Kluwer Dordrecht · Zbl 0802.65122
[3] Babolian, E.; Biazar, J., Solution of a system of linear Volterra equations by Adomian decomposition method, Far East J. Math. Sci., 2, 935-945 (2002) · Zbl 1012.65146
[4] Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to differential equations, Math. Comput. Modeling, 28, 5, 103-110 (1994) · Zbl 0809.65073
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