IJPAM: Volume 44, No. 4 (2008)


Jing-Bo Chen$^1$, Meng-Zhao Qin$^2$, Rudolf Scherer$^3$
$^1$Institute of Geology and Geophysics
Chinese Academy of Sciences
P.O. Box 9825, Beijing, 100080, P.R. CHINA
e-mail: chenjb@mail.igcas.ac.cn
$^2$Institute of Computational Mathematics and Scientific/Engineering Computing
Academy of Mathematics and System Sciences
Chinese Academy of Sciences
P.O. Box 2719, Beijing, 100080, P.R. CHINA
e-mail: qmz@lsec.cc.ac.cn
$^3$Institute for Applied and Numerical Mathematics
University of Karlsruhe (TH)
Karlsruhe, 76128, GERMANY
e-mail: scherer@math.uni-karlsruhe.de

Abstract.Recently multisymplectic discretizations are attracting much attention, because they are the vigorous component of the structure-preserving algorithms. In this paper, the new development in the field of multisymplectic discretizations is systematically described and some very interesting new results are given. Multisymplectic and variational integrators are studied from a comparative point of view. The composition method for constructing higher order multisymplectic integrators is presented. The equivalence of variational integrators to multisymplectic integrators is proved.

Received: February 27, 2008

AMS Subject Classification: 65P10, 65M12

Key Words and Phrases: multisymplectic, variational, structure-preserving, spectral method, composition method, finite element method, Birkhoffian system

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 4