Solving time-dependent differential equations by multiquadric trigonometric quasi-interpolation
Solving time-dependent differential equations by multiquadric trigonometric quasi-interpolation
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通过多重二次三角拟插值求解瞬态微分方程
DOI：
10.1016/j.amc.2014.12.008
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发表时间：
2015-02
影响因子：
4
通讯作者：
Wu Zongmin
中科院分区：
文献类型：
--
作者：
Gao Wenwu;Wu Zongmin
Multiquadric (MQ) quasi-interpolation is a popular method for the numerical solution of differential equations. However, MQ quasi-interpolation is not well suited for the equations with periodic solutions. This is mainly due to the fact that its kernel (the MQ function) is not a periodic function. A reasonable way of overcoming the difficulty is to use a quasi-interpolant whose kernel itself is also periodic in these cases. The paper constructs such a quasi-interpolant. Error estimates of the quasi-interpolant are also provided. The quasi-interpolant possesses many fair properties of the MQ quasi-interpolant (i.e., simplicity, efficiency, stability, etc). Moreover, it is more suitable (than the MQ quasi-interpolant) for periodic problems since the quasi-interpolant as well as its derivatives are periodic. Examples of solving both linear and nonlinear partial differential equations (whose solutions are periodic) by the quasi-interpolant and the MQ quasi-interpolant are compared at the end of the paper. Numerical results show that the quasi-interpolant outperforms the MQ quasi-interpolant for periodic problems.
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DOI：
10.1002/nme.1620121010
发表时间：
1978-01-01
影响因子：
2.9
作者：
BABUSKA, I;RHEINBOLDT, WC
通讯作者：
RHEINBOLDT, WC
影响因子：
2.1
作者：
G. Neubauer
通讯作者：
G. Neubauer
DOI：
10.1016/j.cam.2012.02.028
发表时间：
2012-07
期刊：
J. Comput. Appl. Math.
影响因子：
--
作者：
Wenwu Gao;Zongmin Wu
通讯作者：
Wenwu Gao;Zongmin Wu
影响因子：
2.1
作者：
M. Buhmann
通讯作者：
M. Buhmann
影响因子：
2.9
作者：
Leevan Ling
通讯作者：
Leevan Ling