THE ORDER AND ERROR CONSTANT OF A RUNGE-KUTTA TYPE METHOD FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM

Abstract

Implicit Runge- Kutta methods are used for solving  stiff problems which mostly arise in real life situations. Analysis of  the order, error constant, consistency and convergence will help in determining an effective Runge- Kutta Method (RKM) to use. Due to the loss of  linearity in Runge –Kutta Methods and the fact that the general Runge –Kutta Method  makes no mention of the differential equation makes it impossible to define the order of the method independently of the differential equation.

In this paper, we examine in simpler details how to obtain the order, error constant, consistency  and convergence of a Runge -Kutta Type method (RKTM) when the step number  .