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Home  >  Volume 33

A Class of Self-Starting Multistep Methods with Chebyshev Basis Function for Direct Solution of Second Order ODEs by Olabode B.T and Odeniyan-Fakuade H.F (Pages 79-88)
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Abstract

This article proposed four-step and five-step continuous multistep methods with Chebyshev polynomial as basis functions for the direct solution of system of second order ordinary differential equations. The construction is based on the interpolation of the approximate solution and collocation of derivative function with Chebyshev polynomial as basis functions. The resultant schemes are self-starting, do not need the development of separate predictors, consistent, zero-stable and convergent. The performance of the methods was demonstrated on some numerical examples to show accuracy and efficiency advantages. The numerical results compared favourably with existing method.

                Keywords: Continuous, Multistep Method, Chebyshev Polynomial, Orthogonal Polynomial, Initial Value Problems(IVPs), Ordinary Differential Equations (ODEs).

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