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Vassilios A. Dougalis

Publications and source records attributed to Vassilios A. Dougalis.

4 recordsLinked to original sources
arXiv2021

Numerical solution of internal-wave systems in the intermediate long wave and the Benjamin-Ono regimes

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 waves in a two-layer fluid system in particular physical regimes. The paper focuses on two issues of approximation. First, the spectral Fourier-Galerkin method is used to discretize in space the corresponding periodic initial-value problems, and the error of the semidiscretizations is analyzed. The second issue concerns the numerical generation of solitary-wave solutions of the systems. We use acceleration techniques to improve the computation of the approximate solitary waves and check their performance with numerical examples.

math.NA↗
arXiv2021

Notes on a high order fully discrete scheme for the Korteweg-de vries equation with a time-stepping procedure of Runge-Kutta-composition type

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 order, Runge-Kutta scheme of composition type based on the implicit midpoint rule. We prove $L^{2}$ error estimates for the resulting semidiscrete and the fully discrete approximations.

math.NA↗
arXiv2017

Numerical approximation to Benjamin type equations. Generation and stability of solitary waves

This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is accurately performed with a modified Petviashvili method which includes extrapolation to accelerate the convergence. In order to study the dynamics of the solitary waves the equations are discretized in space with a Fourier pseudospectral collocation method and a fourth-order, diagonally implicit Runge-Kutta method of composition type as time-stepping integrator. The stability of the waves is numerically studied by performing experiments with small and large perturbations of the solitary pulses as well as interactions of solitary waves.

math.NA↗