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Home  >  volume 36 (no1)

Fractional Step Method for the Numerical Integration of Initial Value Problems of Third Order Ordinary Differential Equations by Duromola M.K and Bolarinwa Bolaji (Pages 23-30)
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Abstract

In this paper, we present a new fractional step method whose derivation is by employing the famous Collocation-interpolation approximation technique to derive the main scheme with continuous coefficients, from where additional schemes needed for its implementation were derived.  The implementation strategy of the method is by combining the main scheme and the additional schemes generated from it together in block form as a simultaneous integrator - over non-overlapping intervals - to initial value problems of third order ordinary differential equations. Basic properties of the new methods were investigated and it is observed that the method is consistent, convergence, zero stable and absolutely stable. To test the accuracy and adequacy of our method, we adopted it to solve sample problems and compare with existing method in literature, the numerical results compared favourably.

Mathematics SubjectClassification: 65L80

                Keywords: Fractional step, collocation, interpolation, continuous coefficients, block method, third order differential equations

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