Two-step finite difference schemes of the method of the joint approximation for solving the quasi-linear one-dimensional hyperbolic equations

Authors

  • Валерій Леонідович Бучарський Dnipropetrovsk National University named after O.Gonchar Gagarin ave, 72, Dnipropetrovsk, 49000, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.12368

Keywords:

Method of the joint approximation, finite difference scheme, high order of accuracy

Abstract

In present paper the method of the joint approximation for constructing high order of accuracy finite difference schemes is extended on the case of quasi-linear hyperbolic equations and their systems. The new two-step cost-effective way for constructing compact cost-effective finite difference schemes with unlimited order of accuracy is suggested. This approach is based on the method of the joint approximation and one property of the hyperbolic partial derivatives equations. Finite difference schemes up to eleventh order of temporal and spatial accuracy for the one-dimensional Burgers equation and for system of one-dimension gas dynamic are presented. Results of the solution of the used widely test cases are presented also. The data of the calculations confirm the theoretical results

Author Biography

Валерій Леонідович Бучарський, Dnipropetrovsk National University named after O.Gonchar Gagarin ave, 72, Dnipropetrovsk, 49000

Associate professor

Department of Jet Propulsion System

References

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Published

2013-04-25

How to Cite

Бучарський, В. Л. (2013). Two-step finite difference schemes of the method of the joint approximation for solving the quasi-linear one-dimensional hyperbolic equations. Eastern-European Journal of Enterprise Technologies, 2(4(62), 34–38. https://doi.org/10.15587/1729-4061.2013.12368

Issue

Vol. 2 No. 4(62) (2013): Mathematics and cybernetics - fundamental and applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2014 Валерій Леонідович Бучарський

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