A Discrete Analogue of Energy Integral for a Difference Scheme for Quasilinear Hyperbolic Systems - Applied Mathematics

AM > Vol.9 No.7, July 2018

Applied Mathematics

Volume 9, Issue 7 (July 2018)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.58 Citations

A Discrete Analogue of Energy Integral for a Difference Scheme for Quasilinear Hyperbolic Systems ()

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Download as PDF (Size: 549KB) PP. 789-805

DOI: 10.4236/am.2018.97055 685 Downloads 1,404 Views Citations

Author(s)

R. D. Aloev^1*, Z. K. Eshkuvatov^2,3*, M. U. Khudayberganov¹, N. M. A. Nik Long^3,4

Affiliation(s)

¹Faculty of Mathematics and Mechanics, National University of Uzbekistan (NUUz), Tashkent, Uzbekistan.
²Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), Nilai, Malaysia.
³Institute for Mathematical Research (INSPEM), UPM, Kuala Lumpur, Malaysia.
⁴Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Kuala Lumpur, Malaysia.

ABSTRACT

The class of three-dimensional quasilinear hyperbolic systems is studied. The initial boundary value problem for this class of quasilinear hyperbolic systems is given. By constructing the energy’s integral, a priori estimate for the solution of the initial boundary value problem is obtained. Difference scheme is constructed and an a priori estimate for its solution is obtained. Numerical example exhibits the efficiency and accuracy of the method.

KEYWORDS

Hyperbolic Systems, Stability, Quasilinear Equations

Share and Cite:

Aloev, R. , Eshkuvatov, Z. , Khudayberganov, M. and Nik Long, N. (2018) A Discrete Analogue of Energy Integral for a Difference Scheme for Quasilinear Hyperbolic Systems. Applied Mathematics, 9, 789-805. doi: 10.4236/am.2018.97055.

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