A Comparison Of Explicit Runge-Kutta Methods For Nonstiff IVPs And Their Adaptation For Solving Nonstiff DDES

Many initial value problems are not solvable analytically. In such situation, one of the options is to use numerical methods. In this thesis we present a class of Explicit Runge-Kutta methods. This is a special class of one-step explicit methods.This thesis concentrates on comparison of explicit Runge-Kutta (ERK) methods for non-stiff differential equations and their adaptation to nonstiff single constant delay differential equations. Particular emphasis will be given to the comparison of4th,5th and6th order explicit Runge-Kutta methods. Our comparison will mainly be based on computational cost versus accuracy. There is no method which is efficient to all types of initial value problems. Explicit Runge-Kutta methods are efficient when applied to non-stiff initial value problems. Assuming that the computational cost is proportional to the number of stages in the method, we will compare the ERK methods and show that the higher order methods have a relative advantage over lower order methods. We will show that the higher order methods give better accuracy for less computational effort.At the adaptation for DDEs, we will adapt4th,5th and6th order explicit Runge-Kutta methods. We will assess the performance of the three methods when adapted to single constant delay differential equations. The adaptation is interval wise adaption like the method of steps used to solve DDEs analytically. To interpolate the numerical results so that to enable us go from one interval to the next Hermite interpolation is used. We used3support points for both4th and5th order methods while for the6th order method we took4support points. The6th order method did better than the other two methods adapted.