English

Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval

Numerical Analysis 2020-02-07 v1 Numerical Analysis

Abstract

In this paper we investigate the numerical approximation of the fractional diffusion, advection, reaction equation on a bounded interval. Recently the explicit form of the solution to this equation was obtained. Using the explicit form of the boundary behavior of the solution and Jacobi polynomials, a Petrov-Galerkin approximation scheme is proposed and analyzed. Numerical experiments are presented which support the theoretical results, and demonstrate the accuracy and optimal convergence of the approximation method.

Keywords

Cite

@article{arxiv.2002.02330,
  title  = {Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval},
  author = {Xiangcheng Zheng and V. J. Ervin and Hong Wang},
  journal= {arXiv preprint arXiv:2002.02330},
  year   = {2020}
}

Comments

23 pages, 4 figures