A Clas of A-Stable Runge-Kutta Collocation Methods for the Solution of First Order Ordinary Dierential Equations

Abstract

This paper presented a class of A-stable Runge-Kutta collocation methods with three free parameters for the solution of rst order ordinary dierential equations. Power series was considered as its basis function, adoption of interpolation and collocation of the approximate solution at some selected grid points to give system of equations was also considered. Gaussian Elimination method was used to solve for the unknown parameters and substituted into the approximate solution to give the continuous method. The three cases considered are the Guass, the Lobatto, and the Radau types. Analysis of the methods was made based on order, zero stability, consistence and convergence. The derived schemes were implemented in the Predictor-Corrector mode. Comparison with existing methods showed that the new developed Schemes compete favorably.