Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations

    Authors

    B. E. Moore

    Comments

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    Abbreviated Journal Title

    Math. Comput. Simul.

    Keywords

    Multi-symplectic PDE; Conformal symplectic; Structure-preserving; algorithm; Splitting methods; Modified equations; HAMILTONIAN PDES; NUMERICAL-METHODS; CONSERVATION; SCHEMES; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied

    Abstract

    Conformal symplecticity is generalized to forced-damped multi-symplectic PDEs in 1 + 1 dimensions Since,I conformal multi-symplectic property has a concise form for these equations. numerical algorithms that preserve this property. from a modified equations point of view. are available. In effect. the modified equations for standard multi-symplectic methods and for space-time splitting methods satisfy a conformal multi-symplectic property, and the splitting schemes exactly preserve global symplecticity in a special case. It is also shown that the splitting schemes yield incorrect rates of energy/momentum dissipation, but this IS not the case for standard multi-symplectic schemes. These methods work best. for problems where the dissipation coefficients are small, and a forced-damped semi-linear wave equation is considered as an example Published by Elsevier B.V. on behalf of IMACS.

    Journal Title

    Mathematics and Computers in Simulation

    Volume

    80

    Issue/Number

    1

    Publication Date

    1-1-2009

    Document Type

    Article

    Language

    English

    First Page

    20

    Last Page

    28

    WOS Identifier

    WOS:000271103800004

    ISSN

    0378-4754

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