Article ID Journal Published Year Pages File Type
5776301 Journal of Computational and Applied Mathematics 2017 15 Pages PDF
Abstract
Past work on integration methods that preserve a conformal symplectic structure focuses on Hamiltonian systems with weak linear damping. In this work, systems of PDEs that have conformal symplectic structure in time and space are considered, meaning conformal symplecticity is fully generalized for PDEs. Using multiple examples, it is shown that PDEs with this particular structure have interesting applications. What it means to preserve a multi-conformal-symplectic conservation law numerically is explained, along with presentation of two numerical methods that preserve such properties. Then, the advantages of the methods are briefly explored through applications to linear equations, consideration of momentum and energy dissipation, and backward error analysis. Numerical simulations for two PDEs illustrate the properties of the methods, as well as the advantages over other standard methods.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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