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.
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