Error estimates of a spectral Petrov–Galerkin method for two-sided fractional reaction–diffusion equations

摘要

We study regularity and the spectral method for two-sided fractional diffusion equations with a reaction term. We show that the regularity of the solution in weighted Sobolev spaces can be greatly improved compared to that in standard Sobolev spaces. With this regularity, we prove an optimal error estimate for the spectral Petrov–Galerkin method. Numerical results are presented to verify our theoretical convergence orders.