COMPARISON OF BLOCK IMPLICIT ALGORITHM AND RUNGE KUTTA METHOD FOR THE SOLUTION OF NON LINEAR FIRST ORDER PROBLEMS WITH LEGENDRE POLYNOMIAL AS THE BASIC FUNCTIONS

BLOCK IMPLICIT ALGORITHMS AND RUNGE KUTTA METHODS

Abstract

A family of uniform and non-uniform order Linear
Multistep Block Methods was developed using Legendre Polyno-
mial as the basic functions and reconstructed to its equivalent
Runge { Kutta type Methods. The implicit block method at
k = 3 give a uniform order 6 while implicit block method at
k = 4 gives non uniform order 6  x 9 . The continuous for-
mulation of the method was evaluated at some grid and o grid
points to obtain our implicit block methods. Also both methods
were demonstrated on non-linear rst order initial value prob-
lems (ivps) and the results obtained compared favorably with
the analytic solution