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A new total variation diminishing implicit nonstandard finite difference scheme for conservation laws | ||
| Computational Methods for Differential Equations | ||
| مقاله 5، دوره 2، شماره 2، تیر 2014، صفحه 91-98 اصل مقاله (162.61 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Mohammad Mehdizadeh Khalsaraei* ؛ F. Khodadosti | ||
| University of Maragheh | ||
| چکیده | ||
| In this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of TVD (total variation diminishing) of the solution, is proposed. This scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. Schemes preserving the essential physical property of TVD are of great importance in practice. Such schemes are free of spurious oscillations around discontinuities. Numerical results for Burger's equation is presented. Comparison of numerical results with a classical difference scheme is given. | ||
| کلیدواژهها | ||
| Nonstandard finite difference scheme؛ Total variation diminishing؛ Conservation law؛ Nonlocal approximation | ||
| مراجع | ||
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[10] Mehdizadeh Khalsaraei, M., An improvement on the positivity results for 2-stage explicit RungeKutta methods, J. Comput. Appl. Math 235 (2010), 137-143.
[11] Mehdizadeh Khalsaraei, M., Khodadoosti, F., 2-stage explicit total variation diminishing preserving Runge-Kutta methods, Computational Methods for Differential Equations 1 (2013), 30-38.
[12] P. L. Roe, Approximate Riemann solvers parameter vectors and difference schemes, J. Comput. Phys. 43 (1981), 357-372.
[13] C. W. Shu, Total-variation-diminishing time discretizations, SIAM J. Sci. Statist. Comput 9 (1988), 1073-1084. | ||
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