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.
