CHEBYSHEV-FITTED HYBRID METHODS FOR SOLVING FOURTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

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.