Overview on solving stiff problems using one-step methods

Abstract

Stiff problems in ordinary differential equations can now be solved more routinely. In the past four decades, many researchers were interested in finding effective stiff solution methods. This dissertation is intended for the readers who are interested in solving stiff problems with one-step methods. The focus is on one-step methods, more particularly to implicit Runge-Kutta methods and a recent explicit one-step method. This review explains what stiff differential equations are and what are the requirements for the stiff solution methods. The development of one-step methods in solving stiff problems is outlined. The advantages and disadvantages of each method are also presented. Further, practical implementation of implicit Runge- Kutta methods and the development of one-step methods are discussed briefly. Finally, the dissertation is concluded by presenting a summary of historical reviews of one-step methods in solving stiff problems and some suggestions for future research in this area.