The finite element method for the coupled Schrödinger-KdV equations |
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Authors: | Dongmei Bai Luming Zhang |
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Institution: | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China |
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Abstract: | In this Letter, we employ finite element method to study a periodic initial value problem for the coupled Schrödinger-KdV equations. For the case of one dimension, this problem is reduced to a system of ordinary differential equations by using a semi-discrete scheme. The conservation properties of this scheme, the existence and uniqueness of the discrete solutions, and error estimates are presented. In numerical experiments, the resulting system of ordinary differential equations are solved by Runge-Kutta method at each time level. The superior accuracy of this scheme is shown by comparing the numerical solutions with the exact solutions. |
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Keywords: | 65M60 65N15 65N30 35Q55 |
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