CONSTRUCTION OF SOME IMPLICIT LINEAR MULTI-STEP METHODS INTO RUNGE-KUTTA TYPES METHODS FOR INITIAL VALUE PROBLEMS (IVP) OF FIRST ORDER DIFFERENTIAL EQUATIONS

Abstract

Two implicit Hybrid block methods at step length ????=2 and 3 were derived through collocation procedures. The two derived block methods also reconstructed to an equivalent S stage Runge-Kutta type methods for the solution of ????′=????(????,????). Both methods derived were implemented on the same numerical experiments but Runge-Kutta type methods (RKTM) show its superiority over its equivalent Linear Multi-step Methods of the same value of step length ????