A high-resolution finite-difference scheme for nonuniform grids
The authors derive a higher-order, high-resolution finite-difference scheme for nonuniform grids. These formulas are rigorously derived from Taylor series expansion at nonuniform grid points and they can be applied to approximate first and second spatial derivatives. Based on these formulas, finite difference schemes are constructed with the total variation diminishing constraint applied. The schemes are applied to the one-dimensional convection-diffusion equation and to the two-dimensional nonlinear Burgers equation.
scientific article; zbMATH DE number 770405
scientific article