Restrictive Chebyshev rational approximation and applications to heat-conduction problems

In this paper, we construct a restrictive type of Chebyshev rational approximation. It yields more accurate results and exact values at some selected points. We use this method to approximate the exponential function. We apply this approach to define a new implicit finite difference scheme to parabo...

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Bibliographic Details
Published in:Applied mathematics and computation 2003-04, Vol.136 (2), p.395-403
Main Authors: Elbarbary, Elsayed M.E, Elsayed, Salah M, Youssef, Ismail K, Khodier, Ahmed M.M
Format: Article
Language:English
Subjects:
Approximations and expansions
Chebyshev approximations
Chebyshev rational approximations
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Parabolic partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
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Summary:In this paper, we construct a restrictive type of Chebyshev rational approximation. It yields more accurate results and exact values at some selected points. We use this method to approximate the exponential function. We apply this approach to define a new implicit finite difference scheme to parabolic partial differential equations. This approach will exhibit several advantages features: highly accurate, fast, and the absolute error still very small whatever the exact solution is too large. Stability conditions are obtained and utilized in numerical computations. Finally, some numerical results to describe the performance of this approach are given.
ISSN:0096-3003
1873-5649
DOI:10.1016/S0096-3003(02)00058-9