جستجوی مقالات مرتبط با کلیدواژه « Total variation diminishing » در نشریات گروه « ریاضی »

In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total variation diminishing (TVD). The TVD schemes are robust against the spurious oscillations and preserve the sharpness of the solution near the sharp discontinuities and shocks. We also, prove the positivity and maximum-principle properties for this scheme. The numerical results are presented for both of the advection and Burger’s equation. A comparison of numerical results with some classical limiter functions is also provided.

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.

In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious oscillations around discontinuities.