A Comparative Study of Numerical Methods for Solving the Riccati Equation.

  • Rilwan A. Mustapha Department of Mathematics, Lagos State University, Ojo, Lagos, Nigeria.
  • Gbolahan A. Idowu Department of Mathematics, Lagos State University, Ojo, Lagos State, Nigeria.
  • Michael O. Ajetunmobi Department of Mathematics, Lagos State University, Ojo, Lagos, Nigeria.
Keywords: Laplace Transformation Decomposition Algorithm (LTDA), Riccati equation, Comparison, Homotopy Perturbation Method (HPM) and Adomian Decomposition Method (ADM).

Abstract

In this paper, a Laplace transform decomposition algorithm (LTDA) is used to solve the Riccati equation. Comparison were made among the homotopy perturbation method (HPM), the Adomian decomposition method (ADM) and the proposed method. It is shown that the homotopy perturbation method with a specific convex homotopy is equivalent to the Adomian decomposition method and the Laplace transform decomposition algorithm for solving the Riccati equation.

References

Adomian, G. Nonlinear Stochastic Operator Equations. Academic. , (1986).

Adomian, G. Solving Frontier Problems of Physics: The Decomposition Method. Kluwer, Dordrecht. , (1994).

Adomian, G. Applications of Nonlinear Stochastic System Theory to Physics. Reidel, Dordrecht. , (1987).

Adomian, G. Nonlinear Stochastic Systems Theory and Applications to Physics. Kluwer, Dordrecht. , (1989).

Reid, W. T. Riccati Differential Equations. Academic, New York. , (1972).

Published
2018-08-06
How to Cite
Mustapha, R. A., Idowu, G. A., & Ajetunmobi, M. O. (2018). A Comparative Study of Numerical Methods for Solving the Riccati Equation. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2018, 356 - 363. Retrieved from http://ijmso.unilag.edu.ng/article/view/50
Issue
Vol 2018
Section
Articles

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