| 一阶双曲方程的Legendre—Tau方法 |
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| 引用本文： | 崔凯,马和平.一阶双曲方程的Legendre—Tau方法[J].应用数学与计算数学学报,2009,23(1):42-52. |
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| 作者姓名： | 崔凯 马和平 |
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| 作者单位： | 上海大学理学院,上海,200444 |
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| 摘 要： | 文章采用Legendre—tau方法对一阶双曲方程进行数值求解，此方法可以被有效实施，且可以得到L^2模意义下的最优误差估计，将以往对此类问题的收敛阶估计由O（N^1-τ）提高到O（N^-τ），改进了原有的理论分析结果，数值算例证实了此方法的有效性．
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| 关 键 词： | 一阶双曲方程 Legendre—tau方法 最优估计 |
The Legendre-Tau Method for the First Order Hyperbolic Eequations |
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| Cui Kai,Ma Heping.The Legendre-Tau Method for the First Order Hyperbolic Eequations[J].Communication on Applied Mathematics and Computation,2009,23(1):42-52. |
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| Authors: | Cui Kai Ma Heping |
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| Affiliation: | (Sciences College, Shanghai University, Shanghai 200444, China) |
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| Abstract: | The Legendre-tau method is proposed, analyzed and implemented for the first order hyperbolic equation. By choosing appropriate base functions, the method can be implemented efficiently. Also, the new method enables us to derive the optimal rate of the convergence in L^2-norm, which improved from O（N^1-τ） to OO（N^-τ）. And numerical experiments are given to confirm the throretical result. |
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| Keywords: | first order hyperbolic equation Legendre-Tau method optimal estimate |
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