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Volume 11, Issue 2
Explicit-Implicit Splitting Schemes for Some Systems of Evolutionary Equations

F. Gaspar, A. Grigoriev & P. Vabishchevich

Int. J. Numer. Anal. Mod., 11 (2014), pp. 346-357.

Published online: 2014-11

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  • Abstract

In many applied problems, the individual components of the unknown vector are interconnected and therefore splitting schemes are applied in order to get a simple problem for evaluating unknowns at a new time level. On the basis of additive schemes (splitting schemes), there are constructed efficient computational algorithms for numerical solving the initial value problems for systems of time-dependent PDEs. The present paper deals with computational algorithms that are based on using explicit-implicit approximations in time. Typically, additive operator-difference schemes for systems of evolutionary equations are constructed for operators that are coupled in space. Here we investigate more general problems, where we have coupling of derivatives in time for components of the solution vector.

  • Keywords

Evolutionary problem, splitting scheme, stability of operator-difference schemes, additive operator-difference schemes.

  • AMS Subject Headings

65N06, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-11-346, author = {Gaspar , F.Grigoriev , A. and Vabishchevich , P.}, title = {Explicit-Implicit Splitting Schemes for Some Systems of Evolutionary Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {2}, pages = {346--357}, abstract = {

In many applied problems, the individual components of the unknown vector are interconnected and therefore splitting schemes are applied in order to get a simple problem for evaluating unknowns at a new time level. On the basis of additive schemes (splitting schemes), there are constructed efficient computational algorithms for numerical solving the initial value problems for systems of time-dependent PDEs. The present paper deals with computational algorithms that are based on using explicit-implicit approximations in time. Typically, additive operator-difference schemes for systems of evolutionary equations are constructed for operators that are coupled in space. Here we investigate more general problems, where we have coupling of derivatives in time for components of the solution vector.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/530.html} }
TY - JOUR T1 - Explicit-Implicit Splitting Schemes for Some Systems of Evolutionary Equations AU - Gaspar , F. AU - Grigoriev , A. AU - Vabishchevich , P. JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 346 EP - 357 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/530.html KW - Evolutionary problem, splitting scheme, stability of operator-difference schemes, additive operator-difference schemes. AB -

In many applied problems, the individual components of the unknown vector are interconnected and therefore splitting schemes are applied in order to get a simple problem for evaluating unknowns at a new time level. On the basis of additive schemes (splitting schemes), there are constructed efficient computational algorithms for numerical solving the initial value problems for systems of time-dependent PDEs. The present paper deals with computational algorithms that are based on using explicit-implicit approximations in time. Typically, additive operator-difference schemes for systems of evolutionary equations are constructed for operators that are coupled in space. Here we investigate more general problems, where we have coupling of derivatives in time for components of the solution vector.

Gaspar , F.Grigoriev , A. and Vabishchevich , P.. (2014). Explicit-Implicit Splitting Schemes for Some Systems of Evolutionary Equations. International Journal of Numerical Analysis and Modeling. 11 (2). 346-357. doi:
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