A useful method for understanding discretization error in the numerical solution of ODEs is to compare the system of ODEs with the modified equations, the equations solved by the numerical solution, which are obtained through backward error analysis. Using symplectic integration for Hamiltonian ODEs provides more insight into the modified equations. In this thesis, the ideas of symplectic integration are extended to Hamiltonian PDEs, such that the symplectic structure in both space and time is exactly preserved. This paves the way for the development of a local modified equation analysis solely as a useful diagnostic tool for the study of these types of discretizations. In particular, the multi-symplectic Euler, explicit mid-point, and Prei...
There exist several standard numerical methods for integrating ordinary differential equations. Howe...
Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown ...
Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown ...
A useful method for understanding discretization error in the numerical solution of ODEs is to compa...
Abstract. Multi-symplectic methods have recently been proposed as a generalization of symplectic ODE...
A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation...
Past work on integration methods that preserve a conformal symplectic structure focuses on Hamiltoni...
textabstractMultisymplectic methods have recently been proposed as a generalization of symplectic OD...
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve ...
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve ...
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve ...
A new multi-symplectic formulation of constrained Hamiltonian partial differential equations is pres...
Multi-symplectic methods have recently been cons idered as a generalization of symplectic ODE method...
There exist several standard numerical methods for integrating ordinary differential equations. Howe...
There exist several standard numerical methods for integrating ordinary differential equations. Howe...
There exist several standard numerical methods for integrating ordinary differential equations. Howe...
Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown ...
Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown ...
A useful method for understanding discretization error in the numerical solution of ODEs is to compa...
Abstract. Multi-symplectic methods have recently been proposed as a generalization of symplectic ODE...
A number of conservative PDEs, like various wave equations, allow for a multi-symplectic formulation...
Past work on integration methods that preserve a conformal symplectic structure focuses on Hamiltoni...
textabstractMultisymplectic methods have recently been proposed as a generalization of symplectic OD...
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve ...
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve ...
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve ...
A new multi-symplectic formulation of constrained Hamiltonian partial differential equations is pres...
Multi-symplectic methods have recently been cons idered as a generalization of symplectic ODE method...
There exist several standard numerical methods for integrating ordinary differential equations. Howe...
There exist several standard numerical methods for integrating ordinary differential equations. Howe...
There exist several standard numerical methods for integrating ordinary differential equations. Howe...
Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown ...
Symplectic (area-preserving) integrators for Hamiltonian ordinary differential equations have shown ...