The Linear Transformation of a Block Hybrid Runge-Kutta Type Method for Direct Integration of first and Second Order Initial Value Problems.

Abstract

ABSTRACT The Algebraic structure of a block hybrid Runge-Kutta Type Method (BHRKTM) for the solution of initial value problems was analysed. The co-efficients of the first order Runge-Kutta Type Method (RKTM) of the Butcher table was applied to prove to the second order RKTM. The method of linear transformation and monomorphism was employed to substantiate the uniform order and error constant for the first order BHRKTM and the corresponding extended second order BHRKTM. Two equations evolved that satisfied the Runge- Kutta consistency conditions of second and first order respectively. The Algebraic structure was carefully retained during the transformation.