Journal of Physics A Mathematical and General · 2006 · 230 citations · 127 references
Natural SciencesPhysicsComputational MechanicsDifferential EquationsFluid DynamicsHamiltonian SystemsNumerical AnalysisNumerical Methods For Differential EquationsPartial Differential EquationsSymplectic GeometryVariational FormulationDiscretizationDiscretization Of Partial Differential EquationsHamiltonian FormulationHamiltonian Partial Differential EquationsNonlinear Partial Differential EquationsNumerical Analysis Of Partial Differential EquationsNumerical Solutions Of Partial Differential EquationsVariational Methods In Partial Differential Equations
The paper provides an introduction and survey of conservative discretization methods for Hamiltonian partial differential equations. The emphasis is on variational, symplectic and multi-symplectic methods. The derivation of methods as well as some of their fundamental geometric properties are discussed. Basic principles are illustrated by means of examples from wave and fluid dynamics
127
<i>Linear and Nonlinear Waves</i>
G. B. Whitham, Richard Fowler · Physics Today · 1975 · 8.3K citations
K. J. Whiteman · Physics Bulletin · 1975 · 7.1K citations
Applications of lie groups to differential equations
Acta Applicandae Mathematicae · 1990 · 6.1K citations