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Accelerated finite difference schemes for second order degenerate elliptic and parabolic problems in the whole space


Authors: István Gyöngy and Nicolai Krylov
Journal: Math. Comp. 80 (2011), 1431-1458
MSC (2010): Primary 65M15, 35J70, 35K65
DOI: https://doi.org/10.1090/S0025-5718-2011-02478-6
Published electronically: March 3, 2011
MathSciNet review: 2785464
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Abstract: We give sufficient conditions under which the convergence of finite difference approximations in the space variable of possibly degenerate second order parabolic and elliptic equations can be accelerated to any given order of convergence by Richardson's method.


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Additional Information

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

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

DOI: https://doi.org/10.1090/S0025-5718-2011-02478-6
Keywords: Cauchy problem, finite differences, extrapolation to the limit, Richardson’s method
Received by editor(s): June 4, 2009
Received by editor(s) in revised form: December 31, 2009
Published electronically: March 3, 2011
Additional Notes: The work of the second author was partially supported by NSF grant DMS-0653121
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.