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Zbl 1054.65071
El-Tawil, Magdy A.; Bahnasawi, Ahmed A.; Abdel-Naby, Ahmed
Solving Riccati differential equation using Adomian's decomposition method. (English)
[J] Appl. Math. Comput. 157, No. 2, 503-514 (2004). ISSN 0096-3003

Summary: We suggest a method to solve the matrix Riccati differential equation. The suggested method, which we called multistage Adomian's decomposition method (MADM), can be considered as an extension of the Adomian's decomposition method (ADM) which is very efficient in solving a variety of differential and algebraic equations. The solution is introduced in a recursive form which can be used to obtain the solution for the whole time horizon. Comparisons are made between MADM and the exact solution and further between MADM and different numerical methods.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: comparison of methods; numerical examples; matrix Riccati differential equation; multistage Adomian's decomposition method

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Zentralblatt MATH Berlin [Germany]