An Implicit Exponential Scheme For Solving The Time-Fractional Newell–Whitehead–Segel Equation
Abstract views: 159
/ 
PDF downloads: 67
DOI:
https://doi.org/10.5281/zenodo.16785073Keywords:
Fractional differential equation, finite difference method, conformable derivativeAbstract
This paper presents an implicit exponential finite difference method specifically developed for solving the time-fractional Newell–Whitehead–Segel (NWS) equation, where the conformable fractional derivative is taken into account. Von Neumann stability analysis is employed to evaluate the stability of the proposed numerical scheme. Due to the implicit nature of the scheme, each temporal iteration leads to a system of nonlinear equations. These systems are linearized using Newton's method, facilitating their numerical resolution. To validate the accuracy of the method, numerical results are benchmarked against known exact solutions. The simulation results show that the proposed method is accurate and reliable for solving the complex structure of the time-fractional NWS equation.
References
Athira, K., Narasimlihu, D., Brahmanandam, P.S., 2025. Numerical solutions of time-fractional N–W–S and Burger’s equations using the Tarig Projected Differential Transform Method (TPDTM). Contemporary Mathematics, 6(3): 2907–2928.
Gebril, E., El-Azab, M.S., Sameeh, M., 2024. Chebyshev collocation method for fractional Newell–Whitehead–Segel equation. Alexandria Engineering Journal, 87: 39–46.
Hilal, N., Injrou, S., Karroum, R., 2020. Exponential finite difference methods for solving Newell–Whitehead–Segel equation. Arabian Journal of Mathematics, 9: 367–379.
Inan, B., 2024. The generalized fractional-order Fisher equation: Stability and numerical simulation. Symmetry, 16(4): 393.
Iqbal, N., Albalahi, A., Abdo, M., Mohammed, W., 2022. Analytical analysis of fractional-order Newell–Whitehead–Segel equation: A modified homotopy perturbation transform method. Journal of Function Spaces, 1-10.
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., 2017. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264: 65–70.
Maghsoudi-Khouzani, S., Kurt, A., 2024. New semi-analytical solution of fractional Newell–Whitehead–Segel equation arising in nonlinear optics with non-singular and non-local kernel derivative. Optical and Quantum Electronics, 56: 576.
Patel, H.S., Patel, T., 2021. Applications of fractional reduced differential transform method for solving the generalized fractional-order Fitzhugh-Nagumo equation. International Journal of Applied and Computational Mathematics, 7:188.
Prakash, A., Goyal, M., Gupta, S., 2019. Fractional variational iteration method for solving time-fractional Newell–Whitehead–Segel equation. Nonlinear Engineering, 8(1): 164–171.
Sagar, B., Ray, S.S., 2021. Numerical soliton solutions of fractional Newell–Whitehead–Segel equation in binary fluid mixtures. Computational and Applied Mathematics, 40: 290.
Saha Ray, S. 2020. Nonlinear differential equations in physics. Springer.
Süngü, İ.Ç., Aydın, E., 2022. On the convergence and stability analysis of finite-difference methods for the fractional Newell–Whitehead–Segel equations. Turkish Journal of Mathematics, 46(7): 2806-2818.
Tarasov, V.E., 2010. Fractional dynamics. Higher Education Press, Springer.
Yadav, L.K., Agarwal, G., Gour, M.M., Akgül, A., Misro, M.Y., Purohit, S.D., 2024. A hybrid approach for non-linear fractional Newell–Whitehead–Segel model. Ain Shams Engineering Journal, 15(4): 102645.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 The copyright of the published article belongs to its author.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The journal is licensed under a 