Local energy‐ and momentum‐preserving schemes for Klein‐Gordon‐Schrödinger equations and convergence analysis |
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| Authors: | Jiaxiang Cai Jialin Hong Yushun Wang |
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| Institution: | 1. School of Mathematical Science, Huaiyin Normal University, Huaian, Jiangsu, China;2. Jiangsu Key Laboratory for NSLSCS, School of Mathematical Science, Nanjing Normal University, Nanjing, China;3. State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, CAS, Beijing, China |
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| Abstract: | In this article, we obtain local energy and momentum conservation laws for the Klein‐Gordon‐Schrödinger equations, which are independent of the boundary condition and more essential than the global conservation laws. Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible, we propose local energy‐ and momentum‐preserving schemes for the equations. The merit of the proposed schemes is that the local energy/momentum conservation law is conserved exactly in any time‐space region. With suitable boundary conditions, the schemes will be charge‐ and energy‐/momentum‐preserving. Nonlinear analysis shows LEP schemes are unconditionally stable and the numerical solutions converge to the exact solutions with order  . The theoretical properties are verified by numerical experiments. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1329–1351, 2017 |
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| Keywords: | conservation law convergence analysis Klein‐Gordon‐Schrö dinger equations local structure structure‐preserving algorithm |
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. The theoretical properties are verified by numerical experiments. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1329–1351, 2017