High-Order Grid-Characteristic Method for Systems of Hyperbolic Equations with Piecewise Constant Coefficients

A new approach is considered for increasing the order of accuracy of the grid-characteristic method in the region of coefficient jumps. The approach is based on piecewise polynomial interpolation for schemes of the second and third orders of accuracy for the case where the interface between the medi...

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Bibliographic Details
Published in:Differential equations 2023-07, Vol.59 (7), p.985-997
Main Authors: Khokhlov, N. I., Petrov, I. B.
Format: Article
Language:English
Subjects:
Coefficients
Difference and Functional Equations
Finite difference method
Interpolation
Mathematics
Mathematics and Statistics
Numerical Methods
Ordinary Differential Equations
Partial Differential Equations
Polynomials
Wave propagation
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Summary:A new approach is considered for increasing the order of accuracy of the grid-characteristic method in the region of coefficient jumps. The approach is based on piecewise polynomial interpolation for schemes of the second and third orders of accuracy for the case where the interface between the media is consistent with a finite-difference grid. The method is intended for numerical simulation of the propagation of dynamic wave disturbances in heterogeneous media. Systems of hyperbolic equations with variable coefficients are used to describe the considered physical processes. The description of the numerical method and the results of its testing are given.
ISSN:0012-2661
1608-3083
DOI:10.1134/S001226612307011X