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Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral method for solving partial differential equations. (English) Zbl 0993.65112
Summary: 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 method is also implemented for a detailed comparison so that the performance of the DSC algorithm can be better evaluated. Three two-dimensional 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, wave-number, and Reynolds number. It is found that the DSC algorithm is an accurate, stable and robust approach for solving these PDEs.

MSC:
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
35Q30 Navier-Stokes equations
Software:
Matlab
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References:
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