A multiresolution finite difference scheme for spatially one-dimensional strongly degenerate parabolic equations

Abstract

 An adaptive finite difference method for one-dimensional strongly degenerate parabolic equations is presented. Using an explicit conservative numerical scheme with a third-order Runge-Kutta method for the time discretization, a third-order ENO interpolation for the convective term, and adding a conservative discretization for the diffusive term, we apply the multiresolution method combining the switch between central interpolation or exact computing of numerical flux, and a wavelet transform applied to point values of the solution to control the switch. Applications to mathematical models of sedimentation-consolidation processes and traffic flow with driver reaction illustrate the new method.