Semi-Implicit Scheme to Solve Allen-Cahn Equation with Different Boundary Conditions - American Journal of Computational Mathematics

AJCM > Vol.13 No.1, March 2023

American Journal of Computational Mathematics

Volume 13, Issue 1 (March 2023)

ISSN Print: 2161-1203 ISSN Online: 2161-1211

Google-based Impact Factor: 0.42 Citations

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

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Download as PDF (Size: 6218KB) PP. 122-135

DOI: 10.4236/ajcm.2023.131005 88 Downloads 524 Views

Author(s)

Banan Alqanawi^1*, Musa Adam Aigo²

Affiliation(s)

¹Department of Mathematics, Umm Al-Qura University, Mecca, Saudi Arabia.
²Department of Mathematics, University College in Qunfudah, Umm Al-Qura University, Mecca, Saudi Arabia.

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.

KEYWORDS

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

Share and Cite:

Alqanawi, B. and Aigo, M. (2023) Semi-Implicit Scheme to Solve Allen-Cahn Equation with Different Boundary Conditions. American Journal of Computational Mathematics, 13, 122-135. doi: 10.4236/ajcm.2023.131005.

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