IMPLICIT BLOCK METHODS USING LEGENDRE POLYNOMIALS AS BASIS FUNCTION FOR SOLUTION OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS.

Abstract

The thesis focuses on the derivation, analysis and implementation of 4-step, 5-step, 6-step and 7-step Implicit Block Methods Using Legendre polynomials as basis function for direct solution of fourth order initial value problems of ordinary di erential equations. Method of Collocation of the equation arising from the basis function and the di erential equation at grid points and interpolation of the approximate solution at the chosen points. Taylor series expansion was adopted,to determine the order of the schemes. The derived schemes were implemented in block mode and then applied on some fourth order initial value problems of ordinary di erential equations, the results revealed that the methods converge . The methods were shown to be Consistent and Zero stable, hence Convergent. Accuracy comparison were also made with the existing methods and it was observed that the derived schemes performed favourably with existing ones.