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Additive schemes (splitting schemes) for some systems of evolutionary equations

Author: Petr N. Vabishchevich
Journal: Math. Comp. 83 (2014), 2787-2797
MSC (2010): Primary 65N06, 65M06
Published electronically: March 4, 2014
MathSciNet review: 3246809
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Abstract: On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied problems the individual components of the vector of unknowns are coupled together and then splitting schemes are applied in order to get a simple problem for evaluating components at a new time level. Typically, the additive operator-difference schemes for systems of evolutionary equations are constructed for operators coupled in space. In this paper we investigate more general problems where coupling of derivatives in time for components of the solution vector takes place. Splitting schemes are developed using an additive representation for both the primary operator of the problem and the operator at the time derivative. Splitting schemes are based on a triangular two-component representation of the operators.

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Additional Information

Petr N. Vabishchevich
Affiliation: Nuclear Safety Institute, Russian Academy of Sciences, 52, B. Tulskaya, 115191 Moscow, Russia
Address at time of publication: North-Eastern Federal University, 58, Belinskogo, 677000 Yakutsk, Russia

Keywords: Evolutionary problems, splitting schemes, stability of operator-difference schemes, additive operator-difference schemes
Received by editor(s): December 6, 2011
Received by editor(s) in revised form: January 16, 2013, and February 1, 2013
Published electronically: March 4, 2014
Article copyright: © Copyright 2014 American Mathematical Society

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