| 四阶杆振动方程的两类高精度辛格式 |
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| 引用本文： | 曾文平.四阶杆振动方程的两类高精度辛格式[J].高等学校计算数学学报,2004,26(4):378-384. |
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| 作者姓名： | 曾文平 |
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| 作者单位： | 华侨大学数学系,泉州,362011 |
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| 基金项目： | 国务院侨办自然科学基金项目(02QZR07). |
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| 摘 要： | In this paper, we present two classes of symplectic schemes with high order accuracy for solving four-order rod vibration equation utt uxxxx=0 via the third type generating function method. First, the equation of four order rod vibration is written into the canonical Hamilton system; second, overcoming successfully the essential difficult on the calculus of high order variations derivative, we get the semi-discretization with arbitrary order of accuracy in time direction for the PDEs by the third type generating function method. Furthermore the discretization of the related modified equation of original equation is obtained. Finally, arbitrary order accuracy symplectic schemes are obtained. Numerical results are also presented to show the effectiveness of the scheme, high order accuracy and properties of excellent long-time numerical behavior.
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| 关 键 词： | 高精度辛格式 四阶杆振动方程 PDE |
TWO CLASSES OF SYMPLECTIC SCHEMES WITH HIGH ORDER ACCURACY FOR FOUR-ORDER ROD VIBRATION EQUATION |
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| Zeng Wenping.TWO CLASSES OF SYMPLECTIC SCHEMES WITH HIGH ORDER ACCURACY FOR FOUR-ORDER ROD VIBRATION EQUATION[J].Numerical Mathematics A Journal of Chinese Universities,2004,26(4):378-384. |
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| Authors: | Zeng Wenping |
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| Abstract: | In this paper, we present two classes of symplectic schemes with high order accuracy for solving four-order rod vibration equation utt + uxxxx = 0 via the third type generating function method. First, the equation of four order rod vibration is written into the canonical Hamilton system; second, overcoming successfully the essential difficult on the calculus of high order variations derivative, we get the semi-discretization with arbitrary order of accuracy in time direction for the PDEs by the third type generating function method. Furthermore the discretization of the related modified equation of original equation is obtained. Finally, arbitrary order accuracy symplectic schemes are obtained. Numerical results are also presented to show the effectiveness of the scheme, high order accuracy and properties of excellent long-time numerical behavior. |
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| Keywords: | variation high order accuracy symplectic scheme four order rod vibration equation |
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