Dispersion, group velocity, and multisymplectic discretizations
Abbreviated Journal Title
Math. Comput. Simul.
Box schemes; Leap-frog method; Dispersion relation; Sine-Gordon equation; INTEGRATORS; SCHEMES; EQUATION; PDES; Computer Science, Interdisciplinary Applications; Computer Science, ; Software Engineering; Mathematics, Applied
This paper examines the dispersive properties of multisymplectic discretizations of linear and nonlinear PDEs. We focus on a leapfrog in space and time scheme and the Preissman box scheme. We find that the numerical dispersion relations are monotonic and determine the relationship between the group velocities of the different numerical schemes. The group velocity dispersion is used to explain the qualitative differences in the numerical solutions obtained with the different schemes. Furthermore. the numerical dispersion relation is found to be relevant when determining the ability of the discretizations to resolve nonlinear dynamics. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.
Mathematics and Computers in Simulation
Article; Proceedings Paper
"Dispersion, group velocity, and multisymplectic discretizations" (2009). Faculty Bibliography 2000s. 2104.