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

作　　者：Banan Alqanawi Musa Adam Aigo Banan Alqanawi;Musa Adam Aigo(Department of Mathematics, Umm Al-Qura University, Mecca, Saudi Arabia;Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Mecca, Saudi Arabia)

机构地区：[1]Department of Mathematics, Umm Al-Qura University, Mecca, Saudi Arabia [2]Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Mecca, Saudi Arabia

出　　处：《American Journal of Computational Mathematics》2023年第1期122-135,共14页美国计算数学期刊（英文）

摘　　要：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.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.

关 键 词：Semi-Implicit Schemes Allen-Cahn Equations Finite Difference Sparse System Jacobi Fixed Point GAUSS-SEIDEL 

分 类 号：O17[理学—数学]