A collocation method of lines for two-sided space-fractional advection-diffusion equations with variable coefficients
Provides an efficient numerical method for solving fractional PDEs with variable coefficients, which is important for modeling anomalous diffusion in physics and engineering.
The authors developed a spectral collocation method of lines for solving two-sided space-fractional advection-diffusion equations with variable coefficients, achieving exponential accuracy as demonstrated by four numerical examples.
We present the Method Of Lines (MOL), which is based on the spectral collocation method, to solve space-fractional advection-diffusion equations (SFADEs) on a finite domain with variable coefficients. We focus on the cases in which the SFADEs consist of both left- and right-sided fractional derivatives. To do so, we begin by introducing a new set of basis functions with some interesting features. The MOL, together with the spectral collocation method based on the new basis functions, are successfully applied to the SFADEs. Finally, four numerical examples, including benchmark problems and a problem with discontinuous advection and diffusion coefficients, are provided to illustrate the efficiency and exponentially accuracy of the proposed method.