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Two Kinds of Square-Conservative Integrators for Nonlinear Evolution Equations |
| CHEN Jing-Bo;LIU Hong |
| Institute of Geology and Geophysics, Chinese Academy of Sciences, PO Box 9825, Beijing 100029 |
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| Cite this article: |
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CHEN Jing-Bo, LIU Hong 2008 Chin. Phys. Lett. 25 1168-1171 |
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Abstract Based on the Lie-group and Gauss--Legendre methods, two kinds of square-conservative integrators for square-conservative nonlinear evolution equations are presented. Lie-group based square-conservative integrators are linearly implicit, while Gauss--Legendre based square-conservative integrators are nonlinearly implicit and iterative schemes are needed to solve the corresponding integrators. These two kinds of integrators provide natural candidates for simulating square-conservative nonlinear evolution equations in the sense that these integrators not only preserve the square-conservative properties of the continuous equations but also are nonlinearly stable. Numerical experiments are performed to test the presented integrators.
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| Keywords:
02.60.Cb
02.70.Bf
05.45.Yv
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Received: 14 November 2007
Published: 31 March 2008
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