摘要
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.
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.
基金
Supported by the National Natural Science Foundation of China under grant No 40774069, and the National Hi-Tech Research and Development Programme of China under Grant No 2006AAO9A102-08, and the National Basic Research Programme of China under Grant No 2007CB209603.
