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.