Journal
EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
Volume -, Issue -, Pages -Publisher
GLOBAL SCIENCE PRESS
DOI: 10.4208/eajam.2022-308.300123
Keywords
Momentum-preserving; energy-preserving; high-order; symplectic Runge-Kutta method; Rosenau equation
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Arbitrary high-order numerical schemes conserving the momentum and energy of the generalized Rosenau-type equation are studied in this paper. The momentum-preserving schemes are derived within the symplectic Runge-Kutta method coupled with the standard Fourier pseudo-spectral method. By combining the quadratic auxiliary variable approach, symplectic Runge-Kutta method, and standard Fourier pseudo-spectral method, a class of high-order mass-and energy-preserving schemes for the Rosenau equation is introduced. Various numerical tests demonstrate the performance of the proposed schemes.
Arbitrary high-order numerical schemes conserving the momentum and energy of the generalized Rosenau-type equation are studied. Derivation of momentum preserving schemes is made within the symplectic Runge-Kutta method coupled with the standard Fourier pseudo-spectral method in space. Combining quadratic auxiliary variable approach, symplectic Runge-Kutta method, and standard Fourier pseudo-spectral method, we introduce a class of high-order mass-and energy-preserving schemes for the Rosenau equation. Various numerical tests illustrate the performance of the proposed schemes.
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