|Table of Contents|

A New Fast Compact Time Integrator Method forSolving Klein-Gordon Equations(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2020年02期
Page:
1-5
Research Field:
·数学·
Publishing date:

Info

Title:
A New Fast Compact Time Integrator Method forSolving Klein-Gordon Equations
Author(s):
Huang Jianguo; Wu Bo
School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China
Keywords:
Klein-Gordon equation; compact difference scheme; Hermite interpolation; discrete sine transform
PACS:
O24
DOI:
10.3969/j.issn.1001-4616.2020.02.001
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.

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.

Memo

Memo:
-
Last Update: 2020-05-15