A pseudo-spectral method for a non-local KdV-Burgers equation posed on $\mathbb{R}$

Abstract

In this paper, we present a new pseudo-spectral method to solve the initial value problem associated to a non-local KdV-Burgers equation involving a Caputo-type fractional derivative. The basic idea is, using an algebraic map, to transform the whole real line into a bounded interval where we can apply a Fourier expansion. Special attention is given to the correct computation of the fractional derivative in this setting.

References in corpus (1)

• Fractional Calculus: Integral and Differential Equations of Fractional Order

Cited by in corpus (3)

• Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study
• A Pseudospectral Method for the One-Dimensional Fractional Laplacian on $\mathbb{R}$
• Vanishing viscosity limit of a conservation law regularised by a Riesz-Feller operator