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Award ID contains: 2142500

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  1. ; ; (, SIAM Journal on Mathematics of Data Science)
    Free, publicly-accessible full text available March 31, 2026
  2. ; (, SIAM Journal on Applied Mathematics)
    Free, publicly-accessible full text available February 28, 2026
  3. ; (, Advances in Applied Mathematics and Mechanics)
    Free, publicly-accessible full text available January 1, 2026
  4. ; ; (, Journal of Mathematical Study)
    Free, publicly-accessible full text available December 1, 2025
  5. ; (, Numerical Methods for Partial Differential Equations)
    Full Text Available 
  6. ; (, Physica D: Nonlinear Phenomena)
    Full Text Available 
  7. ; ; (, International Journal of Numerical Analysis and Modeling)
    Full Text Available 
  8. ; ; (, SIAM Journal on Applied Mathematics)
    Full Text Available 
  9. ; ; ; (, Communications on Applied Mathematics and Computation)
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  10. ; (, Discrete & Continuous Dynamical Systems - B)
    In this paper, we propose some second-order stabilized semi-implicit methods for solving the Allen-Cahn-Ohta-Kawasaki and the Allen-Cahn-Ohta-Nakazawa equations. In the numerical methods, some nonlocal linear stabilizing terms are introduced and treated implicitly with other linear terms, while other nonlinear and nonlocal terms are treated explicitly. We consider two different forms of such stabilizers and compare the difference regarding the energy stability. The spatial discretization is performed by the Fourier collocation method with FFT-based fast implementations. Numerically, we verify the second order temporal convergence rate of the proposed schemes. In both binary and ternary systems, the coarsening dynamics is visualized as bubble assemblies in hexagonal or square patterns. 
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