Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral method for solving partial differential equations

This paper explores the utility, tests the accuracy and examines the limitation of the discrete singular convolution (DSC) algorithm for solving partial differential equations (PDEs). The standard Fourier pseudospectral (FPS) method is also implemented for a detailed comparison so that the performance of the DSC algorithm can be better evaluated. Three twodimensional PDEs of different nature, the heat equation, the wave equation and the Navier–Stokes equation, are employed to make our assessment. Either the fourth-order Runge–Kutta or the Crank–Nicolson scheme is employed for the temporal discretization. The DSC algorithm is projected into the Fourier domain for analyzing its numerical resolution. It is demonstrated that the accuracy of the DSC algorithm is controllable. Comprehensive comparisons are given based on a variety of time increment, grid spacing, wavenumber, and Reynolds number. It is found that the DSC algorithm is an accurate, stable and robust approach for solving these PDEs.  2002 Elsevier Science B.V. All rights reserved.