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Mirzaei, Soheila, Shokri, Ali. (1403). Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method. سامانه مدیریت نشریات علمی, 13(2), 479-493. doi: 10.22034/cmde.2024.58979.2500
Soheila Mirzaei; Ali Shokri. "Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method". سامانه مدیریت نشریات علمی, 13, 2, 1403, 479-493. doi: 10.22034/cmde.2024.58979.2500
Mirzaei, Soheila, Shokri, Ali. (1403). 'Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method', سامانه مدیریت نشریات علمی, 13(2), pp. 479-493. doi: 10.22034/cmde.2024.58979.2500
Mirzaei, Soheila, Shokri, Ali. Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method. سامانه مدیریت نشریات علمی, 1403; 13(2): 479-493. doi: 10.22034/cmde.2024.58979.2500

Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method

Computational Methods for Differential Equations
مقاله 9، دوره 13، شماره 2، خرداد 2025، صفحه 479-493    اصل مقاله (495.07 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.58979.2500
نویسندگان
Soheila Mirzaei؛ Ali Shokri*
Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan, Iran.
چکیده
This paper presents a numerical scheme for solving the non-linear time fractional Klein-Gordon equation. To approximate spatial derivatives, we employ the pseudo-spectral method based on Lagrange polynomials at Chebyshev points, while using the finite difference method for time discretization. Our analysis demonstrates that this scheme is unconditionally stable, with a time convergence order of $\mathcal{O}({3 \alpha})$. Additionally, we provide numerical results in one, two, and three dimensions, highlighting the high accuracy of our approach. The significance of our proposed method lies in its ability to efficiently and accurately address the non-linear time fractional Klein-Gordon equation. Furthermore, our numerical outcomes validate the effectiveness of this scheme across different dimensions.
کلیدواژه‌ها
Fractional derivatives؛ Non-linear Klein-Gordon equation؛ Pseudo-spectral method؛ Lagrange polynomials؛ Finite difference scheme
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