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.
