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Benĕ, M. Chalupecky, V. and Mikula, K. (2004) Geometrical Image Segmentation by the AllenCahn Equation. Applied Numerical Mathematics, 51, 187-205.
https://doi.org/10.1016/j.apnum.2004.05.001

has been cited by the following article:

• TITLE: Semi-Implicit Scheme to Solve Allen-Cahn Equation with Different Boundary Conditions

  AUTHORS: Banan Alqanawi, Musa Adam Aigo

  KEYWORDS: Semi-Implicit Schemes, Allen-Cahn Equations, Finite Difference, Sparse System, Jacobi Fixed Point, Gauss-Seidel

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.13 No.1, March 22, 2023

  ABSTRACT: The aim of this paper is to give an appropriate numerical method to solve Allen-Cahn equation, with Dirichlet or Neumann boundary condition. The time discretization involves an explicit scheme for the nonlinear part of the operator and an implicit Euler discretization of the linear part. Finite difference schemes are used for the spatial part. This finally leads to the numerical solution of a sparse linear system that can be solved efficiently.