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Numerical solution for the fifth-order KdV equation by using spectral methods
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| M. Askaripour Lahiji, M. Mirzaei Chalakei, E. Amoupour |
| Department of Mathematics, Astaneh Ashrafieh Branch, Islamic Azad University, Astaneh Ashrafieh, Iran |
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Abstract: (190 Views) |
| Nonlinear wave equations are more difficult to study mathematically and that no general analytical method for their solution exists. It is found that the Exponential Time Differencing (ETD) scheme requires the least steps to achieve a given accuracy, offers a speedy method at calculation time, and has exceptional stability properties in solving a nonlinear equation. This article explains how we applied the exponential integrators (ETDRK4) to semi-linear problems to solve the fifth-order KdV equation. To solve, we define a new integrating factor e^(-ik^5 t) and apply fast Fourier transform (FFT ) for spatial discretization. For this purpose, we solve the diagonal example of the fifth-order KdV equation via the exponential time differencing Runge-Kutta 4 method (ETDRK4). Implementation of the method is proposed by short Matlab programs. |
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| Keywords: Exponential Methods, Integration Factor Methods, Exponential Time Differencing Methods, Runge-Kutta Method. |
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Full-Text [PDF 486 kb]
(61 Downloads)
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Type of Study: Applicable |
Subject:
General
Received: 2023/01/7 | Accepted: 2023/05/28
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