A CLASS OF SEMI-IMPLICIT RATIONAL RUNGE-KUTTA SCHEME FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS WITH DERIVATIVE DISCONTINUITIES.

Abstract

In this thesis, a class of semi-implicit Rational runge-Kutta schemes were developed, analyzed and computerized for solving deferential equations with derivative discontinuities. The method is motivated by variety of application areas of this class of ordinary differential equations; which include electrical transmission networks, nuclear reactions, delay problems and computer aided designs, economy affected by inflation as well as perturbation problems or dynamic processes in industries and technological fields and the need to cater for the deficiencies identified in the adoption of the existing methods of solving this class of differential equations. The development of the schemes, its analysis and implementation on a microcomputer adopt the power series (Taylor and Binomial) expansion and Pade's approximation techniques and Fortran programming respectively. The consistency, convergence and stability properties were investigated, it was discovered that these' schemes converge and were stable. Numerical results of the adoption of the schemes on some sample problems shows that it is effective and efficient ..