A family of non-linear rational integrators for the solution in ordinary differential equations

Özet

In this research work, we derived a Family of Non-Linear rational integrators for the solution of ordinary differential equations. We establish the various integrator formula with an interpolants of order m = 2 and 3 respectively with the use of MAPLE-18 and MATLAB softwares. Our method was compared with an explicit fourth-stage fourth-order Runge-Kutta methods and the Extended Block Integrator for First-Order Stiff and Oscillatory Differential Equations. Our results show good improvement over these recent existing methods compared with, and also ascertain the convergence and consistency of our scheme. Our result shows that our integrator is stable analytically and computationally.