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Home  >  Volume 32 (Nov. 2015)

Collocation Approximation with Legendre Basis Functions to Self-Starting Implicit-Hybrid LMMs For Second Order Stiff Equations by Olabode B. T and Momoh. A. L.(pages 143-152)
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This article presents three-step and four-step implicit hybrid block methods for direct solution of second order stiff differential equations. We achieved this by approach of interpolation and collocation which was applied on one of the orthogonal polynomials precisely Legendre polynomial. Analysis of the methods recovered reveals that they are zero stable, consistent and convergent. The stability domain of the block methods were derived and sketch out. The performances of the methods were tested on numerical examples. The results show that the methods compared creditably well with those of existing methods.

     Keywords: Interpolation, Collocation Approximation, Implicit-Hybrid, Legendre polynomial, Orthogonal          polynomial, Linear Multistep Methods (LMMs), Stiff equations and Ordinary Differential Equations(ODEs)