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.
