Linear, Quasi-Monotonic and Hybrid Grid-Characteristic Schemes for Hyperbolic Equations

Nowadays, the grid-characteristic method is gaining popularity for linear hyperbolic systems of equations. This method is commonly used for the simulation of the wave propagation process in deformable media. This problem requires specific properties of the used numerical method: a high approximation...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2023, Vol.44 (1), p.296-312
Main Authors: Guseva, E. K., Golubev, V. I., Petrov, I. B.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Approximation
Formability
Geometry
Hyperbolic systems
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Numerical methods
Probability Theory and Stochastic Processes
Robustness (mathematics)
Transport equations
Wave propagation
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Summary:Nowadays, the grid-characteristic method is gaining popularity for linear hyperbolic systems of equations. This method is commonly used for the simulation of the wave propagation process in deformable media. This problem requires specific properties of the used numerical method: a high approximation order and a monotonicity. One of the robust monotonicity criteria is the grid-characteristic one, proposed by A. S. Kholodov. This work is devoted to the adaptation of this approach for broaden spatial stencils. On the seven-point stencil the fifth order linear scheme and quasi-monotonic schemes were constructed. Their behavior was evaluated on the linear transport equation with the constant coefficient. Based on the problem with the initial condition of a complex form, the obtained numerical solution was compared with the other ones. The achieved approximation order was calculated based on the numerical experiment results. The detailed analysis was used to choose the scheme with the best behavior.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223010146