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Dispersive and dissipative properties of the fully discrete bicompact schemes of the fourth order of spatial approximation for hyperbolic equations. (English) Zbl 1416.65281

Summary: The Fourier analysis of fully discrete bicompact fourth-order spatial approximation schemes for hyperbolic equations is presented. This analysis is carried out on the example of a model linear advection equation. The results of Fourier analysis are presented as graphs of the dependence of the dispersion and dissipative characteristics of the bicompact schemes on the dimensionless wave number and the Courant number. The dispersion and dissipative properties of bicompact schemes are compared with those of other widely used difference schemes for hyperbolic equations. It is shown that bicompact schemes have one of the best spectral resolutions among the difference schemes being compared.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35L25 Higher-order hyperbolic equations
65T50 Numerical methods for discrete and fast Fourier transforms
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
65L12 Finite difference and finite volume methods for ordinary differential equations

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