NINTH ORDER BLOCK HYBRID INTEGRATORS FOR DIRECT NUMERICAL SOLUTION OF SECOND ORDER DIFFERENTIAL EQUATIONS

Abstract

A ninth order numerical scheme is develped in this work to directly solve second order initial and boundary value problems and via the method of lines for the semi descritization and solution for second order partial differential equations. These schemes are developed via the collocation technique and unified to form a single block of hybrid integrators. The derived method is investigated for its consistency, zero-stability and convergence and found to satisfy these characteristics. Numerical examples shows that the derived method is fond to be efficient in terms of implimentation and less computer time and in terms of accuracy when compared to existing methods in literature.