On Multisymplecticity of Partitioned Runge–Kutta Methods

DOI10.1137/070688468zbMath1172.37030OpenAlexW1979538454MaRDI QIDQ3630373

Brett N. Ryland, Robert I. Mclachlan

Publication date: 28 May 2009

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/070688468

zbMATH Keywords

multisymplecticpartitioned Runge-KuttaLobatto IIIA-IIIBmulti-Hamiltonian

Mathematics Subject Classification ID

Wave equation (35L05) Schrödinger operator, Schrödinger equation (35J10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (11)

On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: energy conservation and multi-symplecticity ⋮ Discrete conservation laws for finite element discretisations of multisymplectic PDEs ⋮ Parallelization, initialization, and boundary treatments for the diamond scheme ⋮ Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs ⋮ Functional equivariance and conservation laws in numerical integration ⋮ A high-order linearly implicit energy-preserving Partitioned Runge-Kutta scheme for a class of nonlinear dispersive equations ⋮ Explicit multi-symplectic extended leap-frog methods for Hamiltonian wave equations ⋮ Derivation of the multisymplectic Crank-Nicolson scheme for the nonlinear Schrödinger equation ⋮ Lobatto IIIA-IIIB discretization of the strongly coupled nonlinear Schrödinger equation ⋮ The Multisymplectic Diamond Scheme ⋮ Multisymplectic box schemes for the complex modified Korteweg–de Vries equation

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