Construction of multisymplectic schemes of any finite order for modified wave equations

DOI10.1063/1.1316062zbMath0992.65145OpenAlexW1971404366MaRDI QIDQ2738287

Meng-Zhao Qin, Ya-Juan Sun

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.1316062

zbMATH Keywords

conservation lawperiodic boundary conditionsHamiltonian formulationlinear wave equationsmultisymplectic schemes

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Wave equation (35L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items

Finite difference scheme of a model for nonlinear wave-wave interaction in ionic media, Multi-symplectic methods for the coupled 1D nonlinear Schrödinger system

Cites Work

• The modified equation approach to the stability and accuracy analysis of finite-difference methods
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Construction of symplectic schemes for wave equations via hyperbolic functions \(\sinh(x)\), \(\cosh(x)\) and \(\tanh(x)\)
• Symplectic integration of Hamiltonian wave equations
• Symplectic approach to the theory of quantized fields. I
• Backward Error Analysis for Numerical Integrators
• Multi-symplectic structures and wave propagation
• Sympletic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation