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 s...

The null space property and the restricted isometry property for a measurement matrix are two basic properties in compressive sampling, and are closely related to the sparse approximation. In this paper, we introduce the sparse approximation property of order s for a measurement matrix A: ‖xs‖2 ≤ D‖Ax‖2 + β σs(x) √ s for all x, where xs is the best s-sparse approximation of the vector x in `, σ...