| 解波动方程的精细积分法及其数值稳定性分析 |
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| 引用本文： | 张明,张晓丹. 解波动方程的精细积分法及其数值稳定性分析[J]. 中国石油大学学报(自然科学版), 2004, 28(6) |
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| 作者姓名： | 张明 张晓丹 |
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| 作者单位： | 1. 石油大学数理系,北京,102249
2. 北京科技大学应用科学学院,北京,100083 |
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| 摘 要： | 将精细积分法用于求解波动方程。详细论述了精细积分法的数值方法,并给出了相应的计算公式。数值算例表明,用精细积分法得到的解与精确解十分吻合,比有限差分法具有更高的精度。同时,推导了解波动方程精细积分法的稳定性条件。与有限差分法相比,精细积分法有更好的数值稳定性。精细积分法的计算公式适用于求解实际工程问题的波动方程,并易于推广应用到二维和三维波动方程的数值求解。
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| 关 键 词： | 波动方程 精细积分法 稳定性条件 数值解 |
Precise integration method for solving wave equation and its numerical stability |
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| ZHANG Ming,ZHANG Xiao-dan. Precise integration method for solving wave equation and its numerical stability[J]. Journal of China University of Petroleum (Edition of Natural Sciences), 2004, 28(6) |
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| Authors: | ZHANG Ming ZHANG Xiao-dan |
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| Affiliation: | ZHANG Ming~1,ZHANG Xiao-dan~2 |
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| Abstract: | A precise integration method was applied to solve wave equation. The principles of the precise integration method were demonstrated in detail, and the corresponding formula for the precise integration method was given. The results of the precise integration method agree well with the theoretical solution and have higher precision than those of the finite difference method. The stability condition of the method was also deduced. The precise integration method is more stable than the finite difference method. The application results demonstrate the validity and applicability of the formula. The formula can be easily used to solve two or three-dimensional wave equation. |
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| Keywords: | wave equation precise integration method stability condition numerical solution |
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