Fifth Order Predictor-Corrector Method for Solving Quadratic Riccati Differential Equations

Year 2017, , 51 - 64, 27.12.2017

Gashu Gadisa Kiltu , Gemadi Roba Kefyalew Hailu

https://doi.org/10.24107/ijeas.349872

Cited By: 2

Abstract

In this paper, fifth
order predictor-corrector method is presented for solving quadratic Riccati
differential equations. First, the interval is discretized and then the method
is formulated by using the Newton’s backward difference interpolation formula.
The stability and convergence of the method have been investigated. To validate
the applicability of the proposed method, three model examples with exact
solutions have been considered and numerically solved by using MATLAB software.
The numerical results are presented in tables and figures for different values
of mesh size h. Pointwise absolute errors and maximum absolute errors are also
estimated. Concisely, the present method gives better result than some existing
numerical methods reported in the literature.  

Keywords

predictor-corrector method, Riccati differential equations, stability analysis

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