In this paper, a new implicit nonstandard finite difference scheme for conserva
tion laws preserving total variation diminishing (TVD) property, is proposed. This
scheme is derived by using nonlocal approximation for nonlinear terms of partial
differential equation. Schemes preserving the essential physical property, such as
TVD are of great importance in practice. Such schemes are free of spurious oscilla-
tions around discontinuities. Numerical results for Burgers’ equation are presented.
.Comparison of numerical results with a classical difference scheme is given
