Parameters spline methods for the solution of hyperbolic equations
Parameters spline methods for the solution of hyperbolic equations
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DOI：
10.1016/j.amc.2008.08.003
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发表时间：
2008-10
期刊：
影响因子：
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通讯作者：
Heng-fei Ding;Yu-xin Zhang
中科院分区：
文献类型：
--
作者：
Heng-fei Ding;Yu-xin Zhang
利用空间上的参数三次样条和时间方向上的紧致有限差分，得到了一类具有混合边界条件的二阶双曲型方程的有限差分格式。对这些方法进行了稳定性分析。结果表明，只要选择合适的三次样条参数，大多数已知的齐次和非齐次情况的方法都可以由我们的方法推导出来。我们还得到了O（h2+τ2h2）和O（h4+τ2h4）的高精度格式。Rashidinia方法的数值比较[J]。Rashidinia等人，双曲方程解的样条法，应用。数学。计算。190(2007)882-886]显示了我们提出的方案的优越性。
In this paper, by using a parameters cubic spline in space and compact finite difference in time direction, we get a class of finite difference schemes for solving second-order hyperbolic equations with mixed boundary conditions. Stability analysis of the methods have been carried out. It has been shown that by suitable choosing the cubic spline parameters most of the previous known methods for homogeneous and non-homogeneous cases can be derived from our methods. We also obtain new high accuracy schemes of O(h2+τ2h2) and O(h4+τ2h4). Numerical comparison with Rashidinia’s method [J. Rashidinia et al., Spline methods for the solutions of hyperbolic equations, Appl. Math. Comput. 190 (2007) 882–886] shows the superiority of our presented schemes.