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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On a new class of additive (splitting) operator-difference schemes


Author: Petr N. Vabishchevich
Journal: Math. Comp. 81 (2012), 267-276
MSC (2010): Primary 65M06, 65M12
Published electronically: June 20, 2011
MathSciNet review: 2833495
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Abstract: Many applied time-dependent problems are characterized by an additive representation of the problem operator. Additive schemes are constructed using such a splitting and are associated with the transition to a new time level on the basis of the solution of more simple problems for the individual operators in the additive decomposition. We consider a new class of additive schemes for problems with additive representation of the operator at the time derivative. In this paper we construct and study the vector operator-difference schemes, which are characterized by a transition from the single initial evolution equation to a system of evolution equations.


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Additional Information

Petr N. Vabishchevich
Affiliation: Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya Sq., 125047 Moscow, Russia
Email: vabishchevich@gmail.com

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02492-0
PII: S 0025-5718(2011)02492-0
Keywords: Evolutionary problems, splitting schemes, the stability of operator-difference schemes, vector additive schemes
Received by editor(s): May 12, 2010
Received by editor(s) in revised form: September 7, 2010
Published electronically: June 20, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.