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

DOI:
https://doi.org/10.1090/S0025-5718-2011-02492-0

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:
https://doi.org/10.1090/S0025-5718-2011-02492-0

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.