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AN ORDER SEVEN CONTINUOUS EXPLICIT METHOD FOR DIRECT SOLUTION OF GENERAL FIFTH ORDER ORDINARY DIFFERENTIAL EQUATIONS

S.J. Kayode

Abstract


This paper provides an explicit continuous method of order seven for direct integration of fifth-order general differential equations without reduction to systems of lower order equations. The explicit method requires no main predictor as a starting value for implementation. In the derivation of the method, collocation and interpolation procedures are adopted using power series as the basis function. The purpose of this work is to produce a high order explicit method that could be used as a predictor for the implementation of implicit methods in predictor-corrector mode in order to enhance the accuracy and efficiency of such methods. The method is symmetric, normalized, consistent and zero-stable. It is suitable for both non-stiff and mildly-stiff problems.

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