HIGHER STAGE INVERSE RUNGE-KUTTA METHODS FOR SOLUTION OF INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This thesis describes the development, analysis and implementation of fifth stage, sixth stage and seventh stage Inverse Runge-kutta methods for the solution of ordinary differential equations (ODEs). The schemes were developed by the adoption of Taylor series expansion techniques and the basic properties were analyzed. The results of the analysis show that the schemes are consistent, convergent and stable. To facilitate the use of the schemes for solution of initial value problem in ordinary differential equations, they were computerized and implemented with some samples initial value problems in ODEs. A comparative analysis of their performance with existing method shows that the proposed schemes are more accurate. The analyses are done on a table and graphical representations are made.