Eighth order Predictor-Corrector Method to Solve Quadratic Riccati Differential Equations

Abstract

In this paper, the eighth-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 Newton’s backward difference interpolation formula. The stability and convergence of the method have been investigated. To validate the applicability of the proposed method, two model examples with exact solutions have been considered and numerically solved. Maximum absolute errors are presented in tables and figures for different values of mesh size h and the present method gives better results than some existing numerical methods reported in the literature.