TENTH ORDER MULTI-STEP PREDICTOR-CORRECTOR METHOD FOR SOLVING THE GENERALIZED QUADRATIC RICCATI DIFFERENTIAL EQUATION

Abstract

In this study, tenth order multi-step predictor-corrector method is formulated for solving the generalized quadratic Riccati differential equations. In order to formulate this method, first, the interval is discretized and then the tenth order predictor and corrector method is formulated by using the Newton’s backward difference interpolation formula. Then after, the tenth order multi step predictor-corrector method formulated. The stability and convergence of the method have been investigated. To demonstrate the efficiency of the proposed method, numerical solutions obtained for three test problems were compared with three other numerical methods, namely, fourth order Runge-Kutta method, fifth order operator-corrector method, and eighth order predictor-corrector method. The numerical results are presented in tables and figures for different mesh sizes. Point wise absolute errors of the proposed method is estimated. For the selected mesh sizes the proposed method is better than the other methods. Based on the numerical results, one can realize that the proposed method is well suited for solving generalized quadratic Riccati differential equation and enables to obtain more accurate solutions than the eight order predictor-corrector method. The numerical stability and convergence of the method coincides with theoretical results. As a result, the introduced method is an efficient and powerful method for solving generalized quadratic Riccati differential equation.