BLOCK NUMERICAL INTEGRATION FORMULAE FOR SOLVING FOURTH ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Abstract

This dissertation focuses on the derivation, analysis and implementation of four-step, five-step, and six-step block numerical integration formulae for solving fourth order initial value problems of ordinary differential equations. The derivation is achieved by adopting interpolation and collocation at some grid points where power series was used as the basis function to obtain a system of linear equations. The system of linear equations is solved using guassian elimination method to obtain the unknown coefficients. The coefficients generated is substituted into the approximate solution to obtain a continuous scheme. The continuous scheme, its first, second and third derivatives are evaluated at some grid points to generate the members of the block methods. The basic properties of the schemes were analyzed. The methods were shown to be consistent and zero stable, hence convergent. The derived schemes were applied on fourth order initial value problem of ordinary differential equations. Comparison was also made with the existing methods and it was found out that the derived schemes compared favourably with existing ones.