Abstract

DIRECT INTEGRATION OF THIRD ORDER INITIAL VALUE PROBLEMS USING NEW RECURSIVE ORTHOGONAL POLYNOMIAL AS BASIS FUNCTION

* E.O. Adeyefa, + R.B. Adeniyi and +R.O. Folaranmi

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Abstract The need for efficient numerical algorithms as an alternative to classical methods of applied mathematics has led to developing numerical methods for the solution of initial value problems in ordinary differential equations. In this paper, our focus in on development of a numerical algorithm which is well suited as integrator of third order initial value problems in ordinary differential equations. A recursive orthogonal polynomial valid in the interval [-1,1] with respect to weight function was constructed and exploited as basis function to formulate a continuous implicit methods, adopting collocation and interpolation techniques. For any numerical integrator to be efficient, ingenious and computationally reliable, it is expected that such is zero stable, consistent and convergent. Findings reveal that this algorithm satisfies these conditions and, comparison of the solution obtained with the exact and existing confirms the desirability of the self-starting methods. Keywords: Collocation, interpolation, new recursive orthogonal polynomial

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