AN ANALYSIS OF ALGEBRAIC PATTERN OF A FIRST ORDER AND AN EXTENDED SECOND ORDER RUNGE-KUTTA TYPE METHOD

Abstract

The algebraic pattern of a 6-Stage Block Hybrid Runge –Kutta Type Methods (BHRKTM) for the solution of Ordinary Differential Equations (ODEs) is carefully analyzed. The analysis of the methods expressed in the Butcher Tableau led to the evolvement of two equations that satisfy the Runge – Kutta consistency conditions. The reason behind the uniform order and error constant for the developed first order and extended second order methods is explained using the theory of linear transformation and monomorphism. The pattern was retained during the transformation.