A class of fixed denominator rational integrators

Abstract

Existing methods such as Niekerk (1987) and Fatunla (1982) are effective but could not handle problem whose initial value is zero. In this paper, we designed and implemented a class of free denominator rational integrators for the solution of initial value problems (IVPs) in ordinary differential equations (ODES), particularly for the case of Stiff and singular problems. The class of integration obtained was found to be consistent and convergent. Our study of the stability characteristics reveal that the integrators are A-stable when m = 0, 1, 2. Their Region of Absolute Stability (RAS) decreases with increasing value of m. Experiments carried out and analyzed with the computer shows encouraging computational results and also show that the rational integrator copes well with all kinds of problem. Key words: Fixed denominator, rational integrators, Jordan curves, A-stable Region of Absolute stability, consistency and convergence.