The decomposition method applied to the Cauchy problem. (English) Zbl 0937.65074
This paper gives a technique for solving initial value differential equations based on an extension to the Picard approach. An expansion is given in terms of Adomian polynomials which are related to certain linear combinations of Taylor series approximations. A simple example is given but there is no material on the speed of convergence and accuracy of this approach.
Reviewer: K.Burrage (Brisbane)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
References:
| [1] | Abbaoui, K. and Cherruault, Y. (1994a), ”Convergence of Adomian’s method applied to differential equations”,Mathematical and Computer Modelling, Vol. 28 No. 5, pp. 103-9. · Zbl 0809.65073 · doi:10.1016/0898-1221(94)00144-8 |
| [2] | DOI: 10.1016/0895-7177(94)00163-4 · Zbl 0822.65027 · doi:10.1016/0895-7177(94)00163-4 |
| [3] | DOI: 10.1016/0895-7177(95)00103-9 · Zbl 0830.65010 · doi:10.1016/0895-7177(95)00103-9 |
| [4] | DOI: 10.1108/eb005812 · Zbl 0697.65051 · doi:10.1108/eb005812 |
| [5] | DOI: 10.1016/0895-7177(93)90233-O · Zbl 0805.65057 · doi:10.1016/0895-7177(93)90233-O |
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