12 citations · 30 across the 9 of their papers we have counts for
9 papers
A numerical method for two-dimensional Boussinesq-Full Dispersion systems modelling internal wave propagation
Angel Durán
The paper is concerned with the numerical approximation of some two-dimensional asymptotic models for the propagation of internal waves in a two-layer system in the form of pde's f…
Numerical solution of internal-wave systems in the intermediate long wave and the Benjamin-Ono regimes
Vassilios A. Dougalis, Angel Durán, Leetha Saridaki
The paper is concerned with the numerical approximation of the Intermediate Long Wave and Benjamin-Ono systems, that serve as models for the propagation of interfacial internal wav…
Notes on a high order fully discrete scheme for the Korteweg-de vries equation with a time-stepping procedure of Runge-Kutta-composition type
Vassilios A. Dougalis, Angel Durán
We consider the periodic initial-value problem for the Korteweg-de Vries equation that we discretize in space by a spectral Fourier-Galerkin method and in time by an implicit, high…
Error estimates for semidiscrete Galerkin and collocation approximations to pseudo-parabolic problems with Dirichlet conditions
Eduardo Abreu, Angel Durán
This paper is concerned with the numerical approximation of the Dirichlet initial-boundary-value problem of nonlinear pseudo-parabolic equations with spectral methods. Error estima…
On the use of spectral discretizations with time strong stability preserving properties to Dirichlet pseudo-parabolic problems
Eduardo Abreu, Angel Durán
This paper is concerned with the approximation of linear and nonlinearinitial-boundary-value problems of pseudo-parabolic equations with Dirichlet boundary conditions. They are dis…
On the multi-symplectic structure of Boussinesq-type systems. II: Geometric discretization
Angel Durán, Denys Dutykh, Dimitrios Mitsotakis
In this paper we consider the numerical approximation of systems of Boussinesq-type to model surface wave propagation. Some theoretical properties of these systems (multi-symplecti…
On the multi-symplectic structure of Boussinesq-type systems. I: Derivation and mathematical properties
Angel Durán, Denys Dutykh, Dimitrios Mitsotakis
The Boussinesq equations are known since the end of the XIXst century. However, the proliferation of various \textsc{Boussinesq}-type systems started only in the second half of the…
Peregrine's system revisited
Angel Durán, Denys Dutykh, Dimitrios Mitsotakis
In 1967 D. H. Peregrine proposed a Boussinesq-type model for long waves in shallow waters of varying depth. This prominent paper turned a new leaf in coastal hydrodynamics along wi…
Notes on the numerical solution of the Benjamin equation
V. A. Dougalis, A. Duran, D. Mitsotakis
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of tw…