[1]黄建国,吴 渤.求解Klein-Gordon方程的新型快速紧致时间积分方法[J].南京师范大学学报(自然科学版),2020,43(02):1-5.[doi:10.3969/j.issn.1001-4616.2020.02.001]
　Huang Jianguo,Wu Bo.A New Fast Compact Time Integrator Method forSolving Klein-Gordon Equations[J].Journal of Nanjing Normal University(Natural Science Edition),2020,43(02):1-5.[doi:10.3969/j.issn.1001-4616.2020.02.001]
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求解Klein-Gordon方程的新型快速紧致时间积分方法()
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《南京师范大学学报》（自然科学版）[ISSN:1001-4616/CN:32-1239/N]

卷:
第43卷
期数:
2020年02期
页码:
1-5
栏目:
·数学·
出版日期:
2020-05-30

文章信息/Info

Title:
A New Fast Compact Time Integrator Method forSolving Klein-Gordon Equations
文章编号:
1001-4616(2020)02-0001-05
作者:
黄建国; 吴 渤
上海交通大学数学科学学院,上海 200240
Author(s):
Huang Jianguo; Wu Bo
School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China
关键词:
Klein-Gordon 方程; 紧致差分格式; Hermite 插值; 离散正弦变换
Keywords:
Klein-Gordon equation; compact difference scheme; Hermite interpolation; discrete sine transform
分类号:
O24
DOI:
10.3969/j.issn.1001-4616.2020.02.001
文献标志码:
A
摘要:
构建了基于 Hermite 插值的快速紧致时间积分方法求解 Klein-Gordon 方程. 该方法先在空间方向上采用四阶紧致差分格式离散得到了一个半离散格式. 然后结合离散正弦变换和常数变易公式给出了半离散格式之解的显示时间积分表示式,并对积分中的非线性源项采用 Hermite 插值逼近,得到了一个全离散格式. 仅需利用前两个时间步的计算结果,就可获得空间和时间方向均为四阶精度的高效算法. 数值模拟的结果验证了该方法的有效性.
Abstract:
This paper is intended to devise a fast compact time integration method based on Hermite interpolation for solving Klein-Gordon equations. The spatial discretization is carried out using the fourth-order compact difference scheme,leading to a semi-discrete problem. Then the solution is expressed explicitly by means of the discrete sine transform and the constant variation formula. Finally,the Hermite interpolation is used to approximate the nonlinear source term,yielding a fully discrete scheme. In particular,if the function values and the derivative function values at two latest historic instants are used for interpolation,we can derive a fourth-order scheme in space and time together. The numerical results verify the effectiveness of the method.

参考文献/References:

[1] DODD R K,EILBECK J C,GIBBON J D,et al. Solitons and nonlinear wave equations[M]. New York:Academic Press,1982.
[2]DRAZIN P G,JOHNSON R S. Solitons:an introduction[M]. Cambridge:Cambridge University Press,1989.
[3]DEHGHAN M,SHOKRI A. Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions[J]. Journal of computational and applied mathematics,2009,230(2):400-410.
[4]STRAUSS W,VAZQUEZ L. Numerical solution of a nonlinear Klein-Gordon equation[J]. Journal of computational physics,1978,28(2):271-278.
[5]DEHGHAN M,GHESMATI A. Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method[J]. Computer physics communications,2010,181(4):772-786.
[6]PEKMEN B,TEZER S M. Differential quadrature solution of nonlinear Klein-Gordon and sine-Gordon equations[J]. Computer physics communications,2012,183(8):1702-1713.
[7]HUANG J,JU L,WU B. A fast compact time integrator method for a family of general order semilinear evolution equations[J]. Journal of computational physics,2019,393:313-336.
[8]HUANG J,JU L,WU B. A fast compact exponential time differencing method for semilinear parabolic equations with Neumann boundary conditions[J]. Applied mathematics letters,2019,94:257-265.
[9]JU L,LIU X,LENG W. Compact implicit integration factor methods for a family of semilinear fourth-order parabolic equations[J]. Discrete and continuous dynamical systems. series B,2014,19(6):1667-1687.
[10]JU L,WANG Z. Exponential time differencing gauge method for incompressible viscous flows[J]. Communications in computational physics,2017,22(2):517-541.
[11]JU L,ZHANG J,ZHU L,et al. Fast explicit integration factor methods for semilinear parabolic equations[J]. Journal of scientific computing,2015,62(2):431-455.
[12]KROGSTAD S. Generalized integrating factor methods for stiff PDEs[J]. Journal of computational physics,2005,203(1):72-88.
[13]NIE Q,WAN F Y M,ZHANG Y T,et al. Compact integration factor methods in high spatial dimensions[J]. Journal of computational physics,2008,227(10):5238-5255.
[14]LELE S K. Compact finite difference schemes with spectral-like resolution[J]. Journal of computational physics,1992,103(1):16-42.
[15]LI M,TANG T,FORNBERG B. A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations. Internat[J]. International journal for numerical methods in fluids,1995,20(10):1137-1151.

备注/Memo

备注/Memo:
收稿日期:2019-08-26.
基金项目:国家自然科学基金面上项目(11571237).
通讯作者:吴渤,博士研究生,研究方向:科学计算. E-mail:sanshiyayan@sjtu.edu.cn
更新日期/Last Update: 2020-05-15