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Journal of Applied Sciences and Environmental Management
World Bank assisted National Agricultural Research Project (NARP) - University of Port Harcourt
ISSN: 1119-8362
Vol. 9, No. 3, 2005, pp. 121-124
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Bioline Code: ja05071
Full paper language: English
Document type: Research Article
Document available free of charge
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Journal of Applied Sciences and Environmental Management, Vol. 9, No. 3, 2005, pp. 121-124
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Superiority of Legendre Polynomials to Chebyshev Polynomial in Solving Ordinary Differential Equation
AKINPELU, FO; ADETUNDE, L A; OMIDIORA, E O.
Abstract
In this paper, we proved the superiority of Legendre polynomial to Chebyshev polynomial in solving first
order ordinary differential equation with rational coefficient. We generated shifted polynomial of Chebyshev,
Legendre and Canonical polynomials which deal with solving differential equation by first choosing Chebyshev polynomial
T*n(X), defined with the help of hypergeometric series T*n(x) =F ( -n, n, 1/2 ;X) and later
choosing Legendre polynomial P*n (x) define by the series P*n (x) = F ( -n, n+1, 1;X); with the help of an auxiliary set
of Canonical polynomials Qk in order to find the superiority between the two polynomials. Numerical examples are given which
show the superiority of Legendre polynomials to Chebyshev polynomials. @JASEM
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© Copyright 2005 - Journal of Applied Sciences & Environmental Management
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