IMPLICIT HYBRID BLOCK NUMEROV-TYPE METHODS FOR DIRECT SOLUTION OF FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this thesis, Implicit Hybrid Numerov-type Methods for Direct Solution of Fourth-order ordinary differential equations (ODEs) have been developed. The interpolation and collocation techniques are applied to generate the main and additional methods. These methods are implemented in both block and predictor-corrector mode. They are applied to solve some numerical test problems ranging from linear to non-linear and problem from ship dynamics. Properties of the methods showed that it is consistent, convergent and zero stable. The methods are coded using MATLAB codes. Numerical examples showed that Block method is more accurate over Predictor-corrector method and compared favourably with the existing methods.