Comparison of different time discretization schemes for solving the Allen–Cahn equation-Reference-Cited by-同舟云学术

Comparison of different time discretization schemes for solving the Allen–Cahn equation

Published:2021-03-17 Issue:0 Volume:0 Page:
ISSN:2191-0294
Container-title:International Journal of Nonlinear Sciences and Numerical Simulation
language:en
Short-container-title:

Author:

Ayub Sana¹,Rauf Abdul¹,Affan Hira²,Shah Abdullah³^ORCID

Affiliation:

1. Department of Mathematics , COMSATS University Islamabad , Islamabad , Pakistan ,

2. Physics Department, College of Science , University of Ha’il , Ha’il , Kingdom of Saudi Arabia ,

3. Department of Mathematics , COMSATS University Islamabad , Park Road , Islamabad 45550 , Pakistan

Abstract

Abstract This article aims to solve the nonlinear Allen–Cahn equation numerically. The diagonally implicit fractional-step θ-(DIFST) scheme is used for the discretization of the time derivative term while the space derivative is discretized by the conforming finite element method. The computational efficiency of the DIFST scheme in terms of CPU time and temporal error estimation is computed and compared with other time discretization schemes. Several test problems are presented to show the effectiveness of the DIFST scheme.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ijnsns-2019-0283/pdf

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