Finite volume methods for unidirectional dispersive wave models

We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular we consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves and their various interactions.Comment: 25 pages, 12 figures, 51 references. Other authors papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Error analysis of implicit and exponential time integration of linear Maxwell\u27s equations

This thesis is concerned with the numerical analysis of some well-known time integration methods, such as implicit collocation methods and exponential integrators, for linear Maxwell\u27s equations in time-domain. The error analysis of time integrators is done both for continuous Maxwell\u27s equations in a semigroup theory framework and for space discrete problem obtained by discretizing Maxwell\u27s equations in space by using discontinuous Galerkin finite element method