Research

Research Areas

• Computational and theoretical mechanics

• Nonlocal theories and peridynamics

• Variational inequalities

• Numerical analysis

Publications

1. Mustapha, I., Alali, B., and Albin, N. Regularity of solutions for nonlocal diffusion equations on periodic distributions. Journal of Integral Equations and Applications 35, 1 (2023), 81–104.

2. Submitted: Burkovska, O., Mustapha, I. An efficient proximal-based approach for solving nonlocal Allen-Cahn equations. Journal of Computational Physics (JCP). October 2024.

3. In preparation: Mustapha, I., Alali, B., and Albin, N. Fourier spectral method for nonlocal equations on bounded domains.

Invited Talks

• Fourier collocation method for nonlocal problems, NSF Mathematical Sciences Graduate Internship Virtual Summer Research Symposium. August 2023.

• Fourier collocation method for nonlocal problems, Mathematics in Computation (MiC) seminar, Oak Ridge National Laboratory, TN. July 2023.

• Fourier multipliers for nonlocal Laplace operators, Graduate Students Seminar, Department of Mathematics, Kansas State University, KS. December 2021.

Contributed Talks

• Fourier continuation method for nonlocal boundary value problems,  Joint Mathematics Meetings (JMM), Seattle Convention Center, Seattle. January 2025.

• Regularity of Solutions for Nonlocal Diffusion Equations on Periodic Distributions, Twelfth Ohio River Analysis Meeting (ORAM 12), University of Cincinnati, OH. March 2023.

• Fourier continuation method for nonlocal boundary value problems. The 9th Annual Meeting of SIAM Central States Section, University of Missouri, Kansas City. October 2024

Poster Presentations

• Fourier collocation method for nonlocal models, The 19th Prairie Analysis Seminar, Kansas State University, Manhattan, KS. November 2023.