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.
