A NEW CLASS OF EXPLICIT RUNGE-KUTTA METHOD FOR INTEGRATION OF INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this thesis, a new class of explicit Runge-Kutta Schemes are developed to solve nonstiff and stiff initial value problems in ordinary differential equations. The method is motivated by the variety of its application in the solution of problems arising from such areas as: population dynamics, pharmaco-kinectic theory, chemical and nuclear reactions, electrical transmission network and other dynamic processes in industries. Its development, analysis and implementation adopts Taylor series expansion, Richardson extrapolation techniques and fortran programming language respectively. The developed schemes are found to be consistent, convergent and Astable. Numerical results and comparative analysis with some standard methods show that the new schemes are accurate, efficient and effective.