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From formal numerical solutions of elliptic PDE's to the true ones
Author(s):
Z.
Wiener;
Y.
Yomdin.
Journal:
Math. Comp.
69
(2000),
197-235.
MSC (1991):
Primary 65N06, 65N15, 35J05
Posted:
August 19, 1999
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Abstract:
We propose a discretization scheme for a numerical solution of elliptic PDE's, based on local representation of functions, by their Taylor polynomials (jets). This scheme utilizes jet calculus to provide a very high order of accuracy for a relatively small number of unknowns involved.
References:
- 1.
- E. Bichuch, and Y. Yomdin, Numerical solution of parabolic equation by the method of high order discretization, The Weizmann Institute of Science, preprint (1994).
- 2.
- M. Gromov, Partial Differential Relations, A Series of Modern Surveys in Mathematics 3 Folge, Band 9, Springer-Verlag, 1986. MR 91e:53047
- 3.
- E. Kochavi, R. Segev, and Y. Yomdin, Numerical Solution of Field Problems by Nonconforming Taylor Discretization., Applied Mathematical Modeling 15 (1991), 152-157.
- 4.
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- 5.
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 -entropy and -capacity of sets in functional spaces, AMS Transl. 17 (2) (1961), 277-364. MR 23:A2031 - 6.
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- 7.
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- 9.
- A. M. Vinogradov, I. S. Krasilshik and V. V. Lychagin, Geometry of jet-spaces and nonlinear differential equations, Moscow, 1977 (Russian).MR 88m:58211
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Additional Information:
Z.
Wiener
Affiliation:
Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
Email:
mswiener@pluto.mscc.huji.ac.il
Y.
Yomdin
Affiliation:
Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
Email:
yomdin@wisdom.weizmann.ac.il
DOI:
10.1090/S0025-5718-99-01147-3
PII:
S 0025-5718(99)01147-3
Received by editor(s):
October 14, 1994
Received by editor(s) in revised form:
May 23, 1997
Posted:
August 19, 1999
Copyright of article:
Copyright
1999,
American Mathematical Society
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