Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

First derivatives estimates for finite-difference schemes

Author(s): István Gyöngy; Nicolai Krylov.
Journal: Math. Comp. 78 (2009), 2019-2046.
MSC (2000): Primary 65M06, 39A70
Posted: February 11, 2009
MathSciNet review: 2521277
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Abstract | References | Similar articles | Additional information

Abstract: We give sufficient conditions under which solutions of discretized in space second-order parabolic and elliptic equations, perhaps degenerate, admit estimates of the first derivatives in the space variables independent of the mesh size.

References:

1.: Hongjie Dong and N.V. Krylov, On the rate of convergence of finite-difference approximations for Bellman equations with constant coefficients, Algebra i Analiz, Vol. 17 (2005), No. 2, 108-132; St. Petersburg Math. J, Vol. 17 (2006), No. 2, 295-313. MR 2159586 (2006f:49050)
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Additional Information:

István Gyöngy
Affiliation: School of Mathematics, University of Edinburgh, King's Buildings, Edinburgh, EH9 3JZ, United Kingdom
Email: gyongy@maths.ed.ac.uk

Nicolai Krylov
Affiliation: 127 Vincent Hall, University of Minnesota, Minneapolis, Minnesota, 55455
Email: krylov@math.umn.edu

DOI: 10.1090/S0025-5718-09-02229-7
PII: S 0025-5718(09)02229-7
Keywords: Cauchy problem, finite differences, first derivatives estimates
Received by editor(s): January 22, 2008
Received by editor(s) in revised form: September 26, 2008
Posted: February 11, 2009
Additional Notes: The work of the second author was partially supported by NSF grant DMS-0653121
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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