Figure 1.
Numerical solution by scheme with limiter (40)
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September
2018, 8(3): 277-289.
doi: 10.3934/naco.2018017
Construction and research of adequate computational models for quasilinear hyperbolic systems
| 1. | National University of Uzbekistan, Faculty of Mathematics, 4, Universitetskaya str., Tashkent, Uzbekistan |
| 2. | Sobolev Institute of Mathematics, 4, Acad. Koptyug str., Novosibirsk, Russia |
In the paper, we study a class of three-dimensional quasilinear hyperbolic systems. For such system, we set the initial boundary value problem and construct the energy integral. We construct the difference scheme and obtain an a priori estimate for its solution.
Mathematics Subject Classification:
Primary: 65N12.
Citation:
Aloev Rakhmatillo, Khudoyberganov Mirzoali, Blokhin Alexander. Construction and research of adequate computational models for quasilinear hyperbolic systems. Numerical Algebra, Control & Optimization,
2018, 8
(3)
: 277-289.
doi: 10.3934/naco.2018017
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References:
| [1] |
R. D. Aloev, Z. K. Eshkuvatov, Sh. O. Davlatov and N. M. A. Nik Long,
Sufficient condition of stability of finite element method for symmetric t-hyperbolic systems with constant coefficients, Computers and Mathematics with Applications, 68 (2014), 1194-1204.
doi: 10.1016/j.camwa.2014.08.019. |
| [2] |
R. D. Aloev, A. M. Blokhin and M. U. Hudayberganov, One class of stable difference schemes for hyperbolic system, American Journal of Numerical Analysis, 2 (2014), 85-89. Google Scholar |
| [3] |
A. M. Blokhin and R. D. Aloev, Energy Integrals and Their Applications to Investigation of Stability of Difference Schemes, Novosibirsk, 1993. 224 p(in Russian). |
| [4] |
S. K. Godunov, Equations of Mathematical Physics, Nauka, Moscow, 1979 (in Russian). |
| [5] |
S. K. Godunov, An interesting class of quasi-linear systems, Dokl. Akad. Nauk SSSR, 139 (1961), 521–523. (in Russian). |
| [6] |
S. K. Godunov and E. I. Romenskii, Elements of Continuum Mechanics and Conservation Laws, Springer-Verlag, New York, 2003.
doi: 10.1007/978-1-4757-5117-8. |
| [7] |
A. Harten,
On the symmetric form of systems of conservation laws with entropy, J. Comp. Phys., 49 (1983), 151-164.
doi: 10.1016/0021-9991(83)90118-3. |
| [8] |
A. I. Vol'pert and S. I. Khudyaev,
On the Cauchy problem for composite systems of nonlinear differential equations, Math. USSR Sb., 16 (1972), 517-544.
doi: 10.1070/SM1972v016n04ABEH001438. |
| [9] |
Yu. S. Zavyalov, B. I. Kvasov and V. L. Miroshnichenko, Methods of Spline Functions, Moscow, Nauka, 1980 (in Russian). |
show all references
References:
| [1] |
R. D. Aloev, Z. K. Eshkuvatov, Sh. O. Davlatov and N. M. A. Nik Long,
Sufficient condition of stability of finite element method for symmetric t-hyperbolic systems with constant coefficients, Computers and Mathematics with Applications, 68 (2014), 1194-1204.
doi: 10.1016/j.camwa.2014.08.019. |
| [2] |
R. D. Aloev, A. M. Blokhin and M. U. Hudayberganov, One class of stable difference schemes for hyperbolic system, American Journal of Numerical Analysis, 2 (2014), 85-89. Google Scholar |
| [3] |
A. M. Blokhin and R. D. Aloev, Energy Integrals and Their Applications to Investigation of Stability of Difference Schemes, Novosibirsk, 1993. 224 p(in Russian). |
| [4] |
S. K. Godunov, Equations of Mathematical Physics, Nauka, Moscow, 1979 (in Russian). |
| [5] |
S. K. Godunov, An interesting class of quasi-linear systems, Dokl. Akad. Nauk SSSR, 139 (1961), 521–523. (in Russian). |
| [6] |
S. K. Godunov and E. I. Romenskii, Elements of Continuum Mechanics and Conservation Laws, Springer-Verlag, New York, 2003.
doi: 10.1007/978-1-4757-5117-8. |
| [7] |
A. Harten,
On the symmetric form of systems of conservation laws with entropy, J. Comp. Phys., 49 (1983), 151-164.
doi: 10.1016/0021-9991(83)90118-3. |
| [8] |
A. I. Vol'pert and S. I. Khudyaev,
On the Cauchy problem for composite systems of nonlinear differential equations, Math. USSR Sb., 16 (1972), 517-544.
doi: 10.1070/SM1972v016n04ABEH001438. |
| [9] |
Yu. S. Zavyalov, B. I. Kvasov and V. L. Miroshnichenko, Methods of Spline Functions, Moscow, Nauka, 1980 (in Russian). |
Figure 2.
Line is exact solution, point-numerical solution by scheme (40)
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