Additive schemes (splitting schemes) for some systems of evolutionary equations
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- by Petr N. Vabishchevich PDF
- Math. Comp. 83 (2014), 2787-2797 Request permission
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.References
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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
- Email: vab@ibrae.ac.ru
- 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
- © Copyright 2014 American Mathematical Society
- Journal: Math. Comp. 83 (2014), 2787-2797
- MSC (2010): Primary 65N06, 65M06
- DOI: https://doi.org/10.1090/S0025-5718-2014-02799-3
- MathSciNet review: 3246809