Restrictive taylor's approximation and parabolic partial differential equations

In this paper we construct a restrictive type of Taylor's approximation of the function f(x) with parameter to be determined. It yields more accurate result, and it has the exact value at certain point. We shall develop a new approach for an explicit method to solve the parabolic partial differ...

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Bibliographic Details
Published in:International journal of computer mathematics 2001-01, Vol.78 (1), p.73-82
Main Authors: Ismail, Hassan N. A., Elbarbary, Elsayed M. E.
Format: Article
Language:English
Subjects:
Approximation of the functions
Approximations and expansions
Exact sciences and technology
Finite difference
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Parabolic partial differential equations
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Restrictive Padé approximation
Sciences and techniques of general use
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Summary:In this paper we construct a restrictive type of Taylor's approximation of the function f(x) with parameter to be determined. It yields more accurate result, and it has the exact value at certain point. We shall develop a new approach for an explicit method to solve the parabolic partial differential equation. This approach will exhibit several advantages features: Highly accurate, fast, and the absolute error still very small whatever the exact solution is too large. The computational results, which are, presented show that computing time and memory space are saved with more accuracy. Stability conditions are obtained and utilized in numerical computations.
ISSN:0020-7160
1029-0265
DOI:10.1080/00207160108805097