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

Jiashu Lu, Mengna Yang and Yufeng Nie

Applied Mathematics and Computation, 2022, vol. 431, issue C

Abstract: This paper considers efficient spectral solutions for weakly singular nonlocal diffusion equations with Dirichlet-type volume constraints. The equation we consider contains an integral operator that typically has a singularity at the midpoint of the integral domain, and the approximation of the integral operator is one of the essential difficulties in solving nonlocal equations. To overcome this problem, two-sided Jacobi spectral quadrature rules are proposed to develop a Jacobi spectral collocation method for nonlocal diffusion equations. A rigorous convergence analysis of the proposed method with the L∞ norm is presented, and we further prove that the Jacobi collocation solution converges to its corresponding local limit as nonlocal interactions vanish. Numerical examples are given to verify the theoretical results.

Keywords: Nonlocal diffusion equations; Spectral collocation methods; Weakly singular kernel; Spectral accuracy; Jacobi quadrature (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322004192

DOI: 10.1016/j.amc.2022.127345

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