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The numerical solution of semidiscrete linear evolution problems on the finite interval using the Unified Transform Method
Jorge Cisneros, Bernard Deconinck
We study a semidiscrete analogue of the Unified Transform Method introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential equat…
High-Frequency Instabilities of Stokes Waves
Ryan Creedon, Bernard Deconinck, Olga Trichtchenko
Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid of arbitrary depth. We investigate the spectral stabili…
The Numerical Unified Transform Method for the Nonlinear Schrödinger equation on the half-line
Xin Yang, Bernard Deconinck, Thomas Trogdon
We implement the Numerical Unified Transform Method to solve the Nonlinear Schrödinger equation on the half-line. For so-called linearizable boundary conditions, the method solves…
The implementation of the unified transform to the nonlinear Schrödinger equation with periodic initial conditions
B. Deconinck, A. S. Fokas, J. Lenells
The unified transform method (UTM) provides a novel approach to the analysis of initial-boundary value problems for linear as well as for a particular class of nonlinear partial di…
The numerical solutions of linear semi-discrete evolution problems on the half-line using the Unified Transform Method
Jorge Cisneros, Bernard Deconinck
We discuss a semi-discrete analogue of the Unified Transform Method, introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential e…
High-Frequency Instabilities of a Boussinesq-Whitham System: A Perturbative Approach
Ryan Creedon, Bernard Deconinck, Olga Trichtchenko
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq-Whitham system. These solutions are shown numerically to exhibit high-frequ…