Comparison of different time discretization schemes for solving the Allen–Cahn equation
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Sana Ayub
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.
Funding source: Higher Education Commission, Pakistan
Award Identifier / Grant number: NRPU-7781
Acknowledgements
The work of S. Ayub is financially supported by Higher Education Commission (HEC) Pakistan under indigenous PhD scholarship scheme. The work of A. Shah and A. Rauf was supported by HEC under NRPU No. 7781.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: The work of A. Shah and A. Rauf was supported by HEC under NRPU No. 7781 while S. Ayub was financially supported by Higher Education Commission (HEC) Pakistan under the indigenous PhD scholarship scheme.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Original Research Articles
- Dynamics of synthetic drug transmission models
- Collision-induced amplitude dynamics of pulses in linear waveguides with the generic nonlinear loss
- Global dissipativity of non-autonomous BAM neural networks with mixed time-varying delays and discontinuous activations
- On the inverse problem for nonlinear strongly damped wave equations with discrete random noise
- A second-order nonlocal regularized variational model for multiframe image super-resolution
- Algebro-geometric integration of a modified shallow wave hierarchy
- Singularity analysis of a 7-DOF spatial hybrid manipulator for medical surgery
- Propagation of diffusing pollutant by kinetic flux-vector splitting method
- Limit cycles in a tritrophic food chain model with general functional responses
- Local and parallel stabilized finite element methods based on full domain decomposition for the stationary Stokes equations
- Stress concentration effect on deflection and stress fields of a master leaf spring through domain decomposition and geometry updation technique
- Electrostatically actuated double walled piezoelectric nanoshell subjected to nonlinear van der Waals effect: nonclassical vibrations and stability analysis
- Traveling wave solutions of the generalized Rosenau–Kawahara-RLW equation via the sine–cosine method and a generalized auxiliary equation method
- A predictor–corrector compact finite difference scheme for a nonlinear partial integro-differential equation
- Parameter inference with analytical propagators for stochastic models of autoregulated gene expression
- DCSK performance analysis of a chaos-based communication using a newly designed chaotic system
- On successive linearization method for differential equations with nonlinear conditions
- Comparison of different time discretization schemes for solving the Allen–Cahn equation
- The homoclinic breather wave solution, rational wave and n-soliton solution to a nonlinear differential equation
- Diversity of interaction phenomenon, cross-kink wave, and the bright-dark solitons for the (3 + 1)-dimensional Kadomtsev–Petviashvili–Boussinesq-like equation
