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Home  >  Volume 32 (Nov. 2015)

Block Multistep Methods with Chebyshev Basis Functions For Second Order ODEs by Olabode B. T and Odeniyan- Fakuade H. F (pages 133-142)
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This article presents two-step and three-step implicit block methods for direct solution of second order stiff differential equations. Techniques of collocation and interpolation were used to generate the methods. One of the orthogonal polynomials precisely Chebyshev polynomial was used as a basis function in the development of the methods and were implemented in block mode. 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 three numerical examples. The results show that the methods compared creditably well with those of existing methods.

Keywords: Interpolation, Collocation Approximation, Chebyshev Polynomial, Orthogonal Polynomial, Linear Multistep Methods (LMMs), Stiff Equations