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math.NA2026
Discontinuity Analysis and Semi-Analytic Spectral Approximation for the Nonlocal Poisson Equation
Thinh Dang, Bacim Alali, Nathan Albin
We study a nonlocal Poisson problem with discontinuous source term and analyze how the regularity of the integral kernel determines the discontinuity structure of the corresponding…
math.NA2025
Fourier Spectral Method for Nonlocal Equations on Bounded Domains
Ilyas Mustapha, Bacim Alali, Nathan Albin
This work introduces efficient and accurate spectral solvers for nonlocal equations on bounded domains. These spectral solvers exploit the fact that integration in the nonlocal for…