Accuracy of classical conservation laws for Hamiltonian PDEs under Runge-Kutta discretizations

DOI10.1007/s00211-008-0204-4zbMath1167.65070OpenAlexW2061842441MaRDI QIDQ1016230

Jialin Hong, Shanshan Jiang, Chun Li

Publication date: 5 May 2009

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-008-0204-4

zbMATH Keywords

error estimatesconservation lawRunge-Kutta methodHamiltonian systemsymplectic integrator

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items

Energy and quadratic invariants preserving (EQUIP) multi-symplectic methods for Hamiltonian wave equations ⋮ Tension spline approach for the numerical solution of nonlinear Klein-Gordon equation

Cites Work

• On the preservation of phase space structure under multisymplectic discretization
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• Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
• Conserved quantities of some Hamiltonian wave equations after full discretization
• Globally conservative properties and error estimation of a multi-symplectic scheme for Schrödinger equations with variable coefficients
• Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations
• Simulating Hamiltonian Dynamics
• Numerical methods for Hamiltonian PDEs
• The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs
• Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
• Geometric integrators for the nonlinear Schrödinger equation
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