CONTINUOUS HYBRID BLOCK METHODS FOR SOLUTION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS USING LEGENDRE-POLYNOMIAL AS BASIS FUNCTION

Abstract

This thesis focuses on the derivation, analysis and implementation of one-step, two-step, three-step and four-step Continuous Hybrid-Block Methods with Legendre polynomial as basis function for direct solution of second order initial value problems of ordinary di erential equation. The approach is based on Collocation of the equation arising from the basis function and the di erential equation at both the grid and o -grid points and interpolation of the approximate solution at the selected points. To estimate the order of the schemes, Taylor series expansion was adopted. The derived schemes were implemented in block mode and then applied on some second order initial value problems of ordinary di erential equations, the results showed that the methods converge as step-size(h) decreases. The methods were shown to be Consistent and Zero stable, hence Convergent. Accuracy comparison was also made with the existing methods and it was found out that the derived schemes compared favourably with existing ones.