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A Discrete Analogue of Energy Integral for a Difference Scheme for Quasilinear Hyperbolic Systems
Faculty of Mathematics and Mechanics, National University of Uzbekistan (NUUz), Tashkent, Uzbekistan
Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), Nilai, Malaysia
Faculty of Mathematics and Mechanics, National University of Uzbekistan (NUUz), Tashkent, Uzbekistan
Institute for Mathematical Research (INSPEM), UPM, Kuala Lumpur, Malaysia
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Kuala Lumpur, Malaysia
- 1 Faculty of Mathematics and Mechanics, National University of Uzbekistan (NUUz), Tashkent, Uzbekistan
- 2 Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), Nilai, Malaysia
- 3 Faculty of Mathematics and Mechanics, National University of Uzbekistan (NUUz), Tashkent, Uzbekistan
- 4 Institute for Mathematical Research (INSPEM), UPM, Kuala Lumpur, Malaysia
- 5 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), Kuala Lumpur, Malaysia
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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.
KeywordsHyperbolic SystemsStabilityQuasilinear Equations
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