A Hamiltonian, explicit algorithm with spectral accuracy for the `good' Boussinesq system

DOI10.1016/0045-7825(90)90046-OzbMath0728.76072OpenAlexW1991762188MaRDI QIDQ805424

T. Ortega, Javier de Frutos, Jesús María Sanz-Serna

Publication date: 1990

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(90)90046-o

zbMATH Keywords

convergencePoisson structureHamiltonian structureNonlinear stabilitytime-discretizationtime-integration schemeFourier transformedHamiltonian, time-discrete, pseudo-spectral schemepartial differential equations in Hamiltonian formsoliton- producing `good' Boussinesq system

Mathematics Subject Classification ID

Finite difference methods applied to problems in fluid mechanics (76M20)

Related Items (15)

Symplectic integration of Hamiltonian wave equations ⋮ Geometric integrators for classical spin systems ⋮ New conservative schemes with discrete variational derivatives for nonlinear wave equations ⋮ A predictor-corrector scheme for the improved Boussinesq equation ⋮ Efficient numerical algorithms for the solution of ``good Boussinesq equation in water wave propagation ⋮ A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation ⋮ Solitary-wave propagation and interactions for the ‘good’ Boussinesq equation ⋮ Energy conservation issues in the numerical solution of the semilinear wave equation ⋮ Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods ⋮ A second order numerical scheme for the solution of the one-dimensional Boussinesq equation ⋮ Symplectic Runge-Kutta and related methods: Recent results ⋮ Order conditions for canonical Runge-Kutta-Nyström methods ⋮ An easily implementable fourth-order method for the time integration of wave problems ⋮ Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods ⋮ A Deuflhard-type exponential integrator Fourier pseudo-spectral method for the ``good Boussinesq equation

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• Symplectic integration of Hamiltonian systems
• Soliton and antisoliton interactions in the ‘‘good’’ Boussinesq equation
• The Exponential Accuracy of Fourier and Chebyshev Differencing Methods

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