Convergence analysis of Jacobi spectral collocation methods for weakly singular nonlocal diffusion equations with volume constraints

作者：

Highlights：

• A Jacobi spectral collocation method is developed for weakly singular nonlocal diffusion equations.

• A two-sided spectral quadrature rule is constructed to overcome the computational difficulties of nonlocal integral.

• A rigorous convergence analysis of the Jacobi collocation method is presented.

• The numerical solution of a nonlocal diffusion equation converges to the correct local limit.

摘要

•A Jacobi spectral collocation method is developed for weakly singular nonlocal diffusion equations.•A two-sided spectral quadrature rule is constructed to overcome the computational difficulties of nonlocal integral.•A rigorous convergence analysis of the Jacobi collocation method is presented.•The numerical solution of a nonlocal diffusion equation converges to the correct local limit.

论文关键词：Nonlocal diffusion equations,Spectral collocation methods,Weakly singular kernel,Spectral accuracy,Jacobi quadrature

论文评审过程：Received 14 April 2022, Revised 6 June 2022, Accepted 17 June 2022, Available online 25 June 2022, Version of Record 25 June 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127345