Multisymplectic structure of numerical methods derived using nonstandard finite difference schemes

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Kosmas, Odysseas^1 ; Papadopoulos, Dimitrios^2

Department of Applied Dynamics, University of Erlangen-Nuremberg, Germany^1

Delta Pi Systems Ltd., 57022 Thessaloniki, Greece^2

关键词: Linear wave equation;    Multi-symplectic;    Multisymplectic structure;    Non-standard finite-differences;    Nonstandard finite difference schemes;    Numerical solution;    Numerical techniques;    Variational principles;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012205/pdf
DOI  :  10.1088/1742-6596/490/1/012205

来源: IOP

【 摘 要 】

In the present work we investigate a class of numerical techniques, that take advantage of discrete variational principles, for the numerical solution of multi-symplectic PDEs arising at various physical problems. The resulting integrators, which use the nonstandard finite difference framework, are also multisymplectic. For the derivation of those integrators, the necessary discrete Lagrangian is expressed at the appropriate discrete jet bundle using triangle and square discretization. The preliminary results obtained by the resulting numerical schemes show that for the case of the linear wave equation the discrete multisymplectic structure is preserved.