Volume 14 - Issue 4 (2) | PP: 94 - 109
Language : English
DOI : https://doi.org/10.31559/glm2024.14.4.2
DOI : https://doi.org/10.31559/glm2024.14.4.2
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Solving first-order systems of linear hyperbolic partial differential equations using fast Fourier transform
Received Date | Revised Date | Accepted Date | Publication Date |
28/8/2024 | 2/10/2024 | 5/11/2024 | 4/2/2025 |
Abstract
In this paper, we address the exact solution of the general first-order systems of linear hyperbolic partial differential equations using the Fourier transformation technique. This transformation converts the system from the physical domain into a system of first-order ordinary differential equations in the frequency domain. Utilizing this method, we then solve the wave equation system in n dimensions. Following the derivation of the exact solution, we introduce a numerical algorithm based on the fast Fourier transform (FFT) to solve the same system numerically. This approach leverages the exact solution obtained in the frequency domain, facilitating efficient and precise numerical computations. To validate the effectiveness of the proposed numerical algorithm, we present numerical experiments. These experiments demonstrate the precision and efficiency of the algorithm when applied to the wave equation system in both two and three dimensions, considering scenarios with continuous and discontinuous initial data.
How To Cite This Article
Zahaykah , Y. & Jwailes , M. (2025). Solving first-order systems of linear hyperbolic partial differential equations using fast Fourier transform. General Letters in Mathematics, 14 (4), 94-109, 10.31559/glm2024.14.4.2
Copyright © 2025, This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.