Discretization of solutions to Poisson’s equation in the Korobov class

A sharp discretization error estimate on the power scale is obtained for the solution of Poisson’s equation with a right-hand side from the Korobov class with the application of Smolyak grid nodes. In some cases, the results coincide in the order of the upper error estimate with earlier results of o...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2013-07, Vol.53 (7), p.896-907
Main Authors: Kudaibergenov, S. S., Sabitova, S. G.
Format: Article
Language:English
Subjects:
Computation
Computational mathematics
Computational Mathematics and Numerical Analysis
Discretization
Errors
Estimates
Euclidean space
Fourier analysis
Mathematical functions
Mathematical models
Mathematics
Mathematics and Statistics
Operators
Optimization algorithms
Partial differential equations
Poisson distribution
Poisson equation
Studies
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Summary:A sharp discretization error estimate on the power scale is obtained for the solution of Poisson’s equation with a right-hand side from the Korobov class with the application of Smolyak grid nodes. In some cases, the results coincide in the order of the upper error estimate with earlier results of other authors, but the discretization operator proposed is simpler.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542513070166