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Solving Riccati differential equation using Adomian’s decomposition method. (English) Zbl 1054.65071
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.

65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
Full Text: DOI
[1] Abbaoui, K.; Cherruault, Y., Convergence of Adomian’s method applied to differential equations, Comput. math appl, 28, 5, 103-109, (1994) · Zbl 0809.65073
[2] Adomian, G.; Sibul, L.H.; Rach, R., Coupled nonlinear stochastic differential equations, J. math. anal. appl, 92, 427-434, (1983) · Zbl 0517.60064
[3] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Boston, MA · Zbl 0802.65122
[4] Anderson, B.D.; Moore, J.B., Optimal control-linear quadratic methods, (1990), Prentice-Hall New Jersey · Zbl 0751.49013
[5] Cherruault, Y., Convergence of Adomian’s method, Kebernetes, 18, 31-38, (1989) · Zbl 0697.65051
[6] F. Dubois, A. Saı̈di, Unconditionally stable scheme for Riccati equation, in: ESAIM Proceedings, vol. 8, 2000, pp. 39-52 · Zbl 0948.34038
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