Abstract:
This research focuses on derivation of Chebyshev-fitted hybrid methods for solving initial
value problems of fourth order ordinary differential equations. In the derivation, Chebyshev
polynomial of first kind was used as basis function. Collocation and Interpolation techniques
were adopted at selected grid and off grid points to generate the system of linear equations
to be solved to be able to obtain the required coefficients for the methods. The derived
methods were implemented in predictor - corrector mode of which the main predictor is of
the same order with the main method. Essential properties of the methods were validated
to ensure that the methods are usable and reliable. The methods were applied to some
numerical examples to ascertain the accuracy of the methods. The results of the numerical
examples show that the methods are accurate and reliable for direct solution of fourth order
ordinary differential equations. Comparison of the results of the methods showed a better
accuracy over the existing methods for fourth order problems in literature.
