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.
Mirzaei, S. and Shokri, A. (2025). Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method. Computational Methods for Differential Equations, 13(2), 479-493. doi: 10.22034/cmde.2024.58979.2500
MLA
Mirzaei, S. , and Shokri, A. . "Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method", Computational Methods for Differential Equations, 13, 2, 2025, 479-493. doi: 10.22034/cmde.2024.58979.2500
HARVARD
Mirzaei, S., Shokri, A. (2025). 'Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method', Computational Methods for Differential Equations, 13(2), pp. 479-493. doi: 10.22034/cmde.2024.58979.2500
CHICAGO
S. Mirzaei and A. Shokri, "Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method," Computational Methods for Differential Equations, 13 2 (2025): 479-493, doi: 10.22034/cmde.2024.58979.2500
VANCOUVER
Mirzaei, S., Shokri, A. Numerical study of the non-linear time fractional Klein-Gordon equation using the Pseudo-spectral method. Computational Methods for Differential Equations, 2025; 13(2): 479-493. doi: 10.22034/cmde.2024.58979.2500
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