HYBRID BLOCK METHODS FOR DIRECT SOLUTION OF THIRD ORDER INITIAL VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS.

Abstract

This research work centres on derivation of linear multistep methods for direct solution of third order ordinary differential equations. Method of collocation and interpolation are adopted to derive the methods. Continuous schemes were developed in each case through which the additional methods needed for implementation of the methods are obtained. The schemes were then combined and expressed as a single matrix. The order, error constant, zero stability and convergence of the block were also examined. The methods were applied on four numerical examples. The results show that the methods are accurate and efficient for direct solution of third order ordinary differential equations.