|
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
Retrieve article in:
PDF
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)
- 2.
- Hongjie Dong and N.V. Krylov, On the rate of convergence of finite-difference approximations for degenerate linear parabolic equations with
 and  coefficients, Electron. J. Diff. Eqns., Vol. 2005(2005), No. 102, pp. 1-25. http://ejde.math.txstate.edu MR 2162263 (2006i:35008) - 3.
- Hongjie Dong and N.V. Krylov, On the rate of convergence of finite-difference approximations for parabolic Bellman equations with Lipschitz coefficients in cylindrical domains, Applied Math. and Optimization, Vol. 56 (2007), No. 1, 37-66. MR 2334605 (2008e:65240)
- 4.
- I. Gyöngy, Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. II, Potential Anal., Vol. 11 (1999), No. 1, 1-37. MR 1699161 (2000g:60106)
- 5.
- I. Gyöngy and N.V. Krylov, Accelerated convergence of finite difference schemes for second order parabolic and elliptic PDEs, in preparation.
- 6.
- N.V. Krylov, A priori estimates of smoothness of solutions to difference Bellman equations with linear and quasi-linear operators, Math. Comp., Vol. 76 (2007), 669-698. MR 2291833 (2008e:65250)
- 7.
- N.V. Krylov, On factorizations of smooth nonnegative matrix-values functions and on smooth functions with values in polyhedra, Applied Math. Optimiz., Vol. 58 (2008), No. 3, 373-392. MR 2456852
- 8.
- W. Littman, Résolution du problème de Dirichlet par la méthode des différences finies, C. R. Acad. Sci. Paris, Vol. 247 (1958), 2270-2272. MR 0107748 (21:6470)
- 9.
- J. von Neumann and R.D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks, J. Appl. Phys., Vol. 21 (1950), 232-237. MR 0037613 (12:289b)
- 10.
- Hyek Yoo, Semi-discretization of stochastic partial differential equations on
 by a finite-difference method, Math. Comp., Vol. 69 (2000), No. 230, 653-666. MR 1654030 (2000i:65129)
Similar Articles:
Retrieve articles in Mathematics of Computation
with MSC
(2000):
65M06, 39A70
Retrieve articles in all Journals with MSC
(2000):
65M06, 39A70
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.
|
Comments: webmaster@ams.org