| 解非线性二阶双曲型方程的一种新数值方法 |
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| 引用本文： | 谢树森. 解非线性二阶双曲型方程的一种新数值方法[J]. 系统科学与数学, 1998, 18(4): 501-506 |
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| 作者姓名： | 谢树森 |
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| 作者单位： | 青岛海洋大学应用数学系!青岛，266003 |
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| 摘 要： | 本文建立了解二阶双曲型方程的一种新数值方法一再生核函数法．利用再生核函数，直接给出每个离散时间层上近似解的显式表达式．此方法的优点是：计算格式绝对稳定，且可显式求解；利用显式表达式，可实现完全并行计算等文中对近似解的收敛性和稳定性进行了理论分析，并给出数值算例．
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| 关 键 词： | 双曲型方程 再生核 误差估计 |
A NEW NUMERICAL METHOD FOR SECOND ORDER NONLINEAR HYPERBOLIC EQUATIONS |
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| Xie Shusen. A NEW NUMERICAL METHOD FOR SECOND ORDER NONLINEAR HYPERBOLIC EQUATIONS[J]. Journal of Systems Science and Mathematical Sciences, 1998, 18(4): 501-506 |
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| Authors: | Xie Shusen |
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| Affiliation: | (Department of Applied Mathematics, Ocean University of Qingdao, Qingdao 266003 ) |
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| Abstract: | In this paper, a reproducing kernel function method for numerically solving second order hyperbolic equations is devised. By using the reproducing kernel function, the approximate solution at each discrete time level is given with explicit formula. The advantage of this method is that the scheme is'absolutely stable, and is explicitly solvable as well. Using the explicit formula, computations run fully parallel. The theoretical analysis of stability and convergence is presented. Some numerical results are also given. |
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| Keywords: | Hyperbolic equation reproducing kernel error estimates. |
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