A pseudo-spectral method for a non-local KdV-Burgers equation posed on $\mathbb R$
This work provides a numerical method for a specific class of fractional PDEs, but it is incremental as it adapts existing pseudo-spectral techniques to a particular equation.
The paper develops a pseudo-spectral method for solving a non-local KdV-Burgers equation with a Caputo fractional derivative on the real line, using an algebraic mapping to a bounded interval for Fourier expansion. The method accurately computes the fractional derivative in this transformed setting.
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.