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Home  >  Volume 46 (May, 2018)

8. A DECOMPOSITION ALGORITHM FOR THE APPROXIMATE SOLUTION OF GENERALIZED RICCATI DIFFERENTIAL EQUATION. by Osilagun J.A., Taiwo O. A. and Akinfenwa O.A. Volume 46 (May, 2018 Issue), pp59 –64
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A DECOMPOSITION ALGORITHM FOR THE APPROXIMATE SOLUTION OF GENERALIZED RICCATI DIFFERENTIAL EQUATION.

Osilagun J.A., Taiwo O. A. and Akinfenwa O.A.

Department of Mathematics, Univesity of Lagos, Akoka-Yaba, Nigeria.

Department of mathematics, university of Ilorin, Ilorin, Nigeria

Abstract

In this paper, we present a Decomposition Algorithm for an appropriate solution of generalized Riccati differential equation without considering the special polynomials such as Adomian, Bell’s, Chebyshev and Legendre polynomials. The proposed decomposition algorithm is A- stable and gives the results as an infinite series that converges rapidly to the exact solution. Comparisons were made by the developed algorithm between Adomians’s decomposition method, variational iteration method, 4th order Runge-Kutta method and the exact solution which shows the effectiveness, accuracy and simplicity of the algorithm. Numerical examples are given to illustrate the accuracy and efficiency of this method. The algorithm can be extended further to solve other non-linear problems of any order.

Keywords: Riccati Equations, Variational Iteration Method, Runge-Kuta Method, Decomposition, Accuracy, Efficiency.

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