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

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.