An explicit stable finite difference method for the Allen–Cahn equation

Lee, Chaeyoung; Choi, Yongho; Kim, Junseok

doi:10.1016/j.apnum.2022.08.006

Cited by 11 publications

(1 citation statement)

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“…We call The nonlinearities in the PDE are trivial ( 3 u u − ) to deal with if we choose an explicit time integration method for the nonlinear part and backward time integration for the linear part, all the mathematical details for the nonlinear discretization of Allen Cahan equation is presented in subsection 3.1, we call this method a semi-implicit backward scheme. If we choose an explicit time integration method for Allen-Cahn equation, such as the Forward Euler finite difference, there is a strict restriction on the time step size to get convergence, for further details see [16]. Since the problem is a nonlinear dynamical system, for stability reasons, we propose taken explicitly a semi-implicit backward Euler scheme with the nonlinear part (as presented in subsection 3.1).…”

Section: Semi-implicit Method: Matrix Formulationmentioning

confidence: 99%

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

Alqanawi¹,

Aigo²

2023

AJCM

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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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Section: Semi-implicit Method: Matrix Formulationmentioning

confidence: 99%