REFORMULATION OF TWO STEP IMPLICIT LINEAR MULTI-STEP BLOCK HYBRID METHOD INTO RUNGE KUTTA TYPE METHOD FOR THE SOLUTION OF SECOND ORDER INITIAL VALUE PROBLEM (IVP)

Abstract

Second-order ordinary differential equations (ODEs) is unavoidable in scientific and engineering fields. This research focuses on the reformulation of two-step implicit linear multistep block hybrid method into a seven-stage Runge-Kutta type method for the solution of second-order initial value problems (IVPs). A two-step, four-off-grid-point implicit block hybrid collocation method for first-order initial value problems was derived. Its order and error constants were determined, which shows that the schemes were of order 8, 8, 8, 8, 8 and 9 with respective error constants of , , , , . The derived block method was reformulated into a seven-stage Runge-Kutta type method (RKTM) for the solution of first-order ordinary differential equations; this reformulation was extended to handle the required second-order ordinary differential equations. The second-order Runge- Kutta-type method derived was implemented on numerical experiments. The method was found to be better than existing methods in the literature.