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 ..
