Regularized additive operator-difference schemes |
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Authors: | P N Vabishchevich |
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Institution: | 1.Institute of Mathematical Modeling,Russian Academy of Sciences,Moscow,Russia |
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Abstract: | The construction of additive operator-difference (splitting) schemes for the approximate solution Cauchy problem for the first-order
evolutionary equation is considered. Unconditionally stable additive schemes are constructed on the basis of the Samarskii
regularization principle for operator-difference schemes. In the case of arbitrary multicomponent splitting, these schemes
belong to the class of additive full approximation schemes. Regularized additive operator-difference schemes for evolutionary
problems are constructed without the assumption that the regularizing operator and the operator of the problem are commutable.
Regularized additive schemes with double multiplicative perturbation of the additive terms of the problem’s operator are proposed.
The possibility of using factorized multicomponent splitting schemes, which can be used for the approximate solution of steadystate
problems (finite difference relaxation schemes) are discussed. Some possibilities of extending the proposed regularized additive
schemes to other problems are considered. |
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Keywords: | |
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