A new finite variable difference method with application to locally exact numerical scheme
A new finite difference scheme for the one-dimensional advection-diffusion-reaction equation is presented and studied. The essence of this method consists of determining the spatial difference, which minimizes the total variance of the solution under the condition that the scheme is always stable. The derived approximation is applied to locally exact numerical schemes (i.e. such that the solution is locally fitted by exponential functions). The optimal spatial differencing is derived in terms of the local mesh Reynold's numbers. Numerous numerical experiments confirm the theoretical findings for large ranges of the parameters.
scientific article; zbMATH DE number 881888