Runge-Kutta methods with minimal dispersion and dissipation for problems arising from computational acoustics. (English) Zbl 1063.65113

Summary: A new Runge-Kutta method with minimal dispersion and dissipation error is developed. The Chebyshev pseudospectral method is utilized using spatial discretization and a new fourth-order six-stage Runge-Kutta scheme is used for time advancing. The proposed scheme is more efficient than the existing ones for acoustic computations.


65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
76Q05 Hydro- and aero-acoustics
76M22 Spectral methods applied to problems in fluid mechanics
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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