Long time error analysis of the fourth‐order compact finite difference methods for the nonlinear
            Klein–Gordon
            equation with weak nonlinearity

Yue Feng

doi:10.1002/num.22558

Long time error analysis of the fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation with weak nonlinearity

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22558 ◽

2020 ◽

Vol 37 (1) ◽

pp. 897-914

Author(s):

Yue Feng

Keyword(s):

Finite Difference ◽

Fourth Order ◽

Gordon Equation ◽

Finite Difference Methods ◽

Time Error ◽

Weak Nonlinearity ◽

Long Time ◽

Klein Gordon ◽

Difference Methods ◽

Klein Gordon Equation

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Optimal error estimates of fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation in the nonrelativistic regime

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22664 ◽

2020 ◽

Author(s):

Teng Zhang ◽

Tingchun Wang

Keyword(s):

Finite Difference ◽

Error Estimates ◽

Fourth Order ◽

Gordon Equation ◽

Finite Difference Methods ◽

Optimal Error Estimates ◽

Optimal Error ◽

Klein Gordon ◽

Difference Methods ◽

Klein Gordon Equation

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Long Time Error Analysis of Finite Difference Time Domain Methods for the Nonlinear Klein-Gordon Equation with Weak Nonlinearity

Communications in Computational Physics ◽

10.4208/cicp.2019.js60.03 ◽

2019 ◽

Vol 26 (5) ◽

pp. 1307-1334 ◽

Cited By ~ 1

Author(s):

Weizhu Bao

Keyword(s):

Finite Difference ◽

Time Domain ◽

Finite Difference Time Domain ◽

Gordon Equation ◽

Time Error ◽

Weak Nonlinearity ◽

Long Time ◽

Klein Gordon ◽

Difference Time ◽

Klein Gordon Equation

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The Finite Difference Methods for –Nonlinear Klein Gordon Equation

IOSR Journal of Engineering ◽

10.9790/3021-031150105 ◽

2013 ◽

Vol 3 (11) ◽

pp. 01-05

Author(s):

Fadhil H. Easif

Keyword(s):

Finite Difference ◽

Gordon Equation ◽

Finite Difference Methods ◽

Klein Gordon ◽

Difference Methods ◽

Klein Gordon Equation

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Regularised Finite Difference Methods for the Logarithmic Klein-Gordon Equation

East Asian Journal on Applied Mathematics ◽

10.4208/eajam.140820.250820 ◽

2021 ◽

Vol 11 (1) ◽

pp. 119-142

Author(s):

Jingye Yan

Keyword(s):

Finite Difference ◽

Gordon Equation ◽

Finite Difference Methods ◽

Klein Gordon ◽

Difference Methods ◽

Klein Gordon Equation

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The Finite Difference Methods for φ4 Klein-Gordon Equation

AL-Rafidain Journal of Computer Sciences and Mathematics ◽

10.33899/csmj.2008.163970 ◽

2008 ◽

Vol 5 (2) ◽

pp. 47-63

Author(s):

Saad Manaa ◽

Laya Hawell

Keyword(s):

Finite Difference ◽

Gordon Equation ◽

Finite Difference Methods ◽

Klein Gordon ◽

Difference Methods ◽

Klein Gordon Equation

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Two regularized energy-preserving finite difference methods for the logarithmic Klein-Gordon equation

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2021.113478 ◽

2021 ◽

pp. 113478

Author(s):

Jingye Yan ◽

Xu Qian ◽

Hong Zhang ◽

Songhe Song

Keyword(s):

Finite Difference ◽

Gordon Equation ◽

Finite Difference Methods ◽

Klein Gordon ◽

Difference Methods ◽

Klein Gordon Equation

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Efficient high-order finite difference methods for nonlinear Klein–Gordon equations. I: Variants of the phi-four model and the form-I of the nonlinear Klein–Gordon equation

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2015.2.9 ◽

2015 ◽

Vol 20 (2) ◽

pp. 274-290 ◽

Cited By ~ 1

Author(s):

Ascensión Hernández Encinas ◽

◽

Jesus Martín-Vaquero ◽

Araceli Queiruga-Dios ◽

Víctor Gayoso-Martínez ◽

...

Keyword(s):

Finite Difference ◽

Gordon Equation ◽

Finite Difference Methods ◽

High Order ◽

Klein Gordon ◽

Difference Methods ◽

High Order Finite Difference ◽

Klein Gordon Equation

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Uniform error bounds of a time-splitting spectral methods for the long-time dynamics of the nonlinear Klein-Gordon equation with weak nonlinearity

10.1090/mcom/3694 ◽

2021 ◽

Author(s):

Weizhu Bao ◽

Yue Feng ◽

Chunmei Su

Keyword(s):

Error Bounds ◽

Spectral Methods ◽

Gordon Equation ◽

Weak Nonlinearity ◽

Time Dynamics ◽

Long Time ◽

Klein Gordon ◽

Time Splitting ◽

Long Time Dynamics ◽

Klein Gordon Equation

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Analysis of Nanostructural Waveguides Using Fourth-Order Accurate Finite Difference Methods with Nonuniform Scheme

Chinese Physics Letters ◽

10.1088/0256-307x/26/1/014205 ◽

2009 ◽

Vol 26 (1) ◽

pp. 014205 ◽

Cited By ~ 3

Author(s):

Ji Yang ◽

Yun Bin-Feng ◽

Hu Guo-Hua ◽

Cui Yi-Ping

Keyword(s):

Finite Difference ◽

Fourth Order ◽

Finite Difference Methods ◽

Difference Methods

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A fourth-order exponential wave integrator Fourier pseudo-spectral method for the Klein–Gordon equation

Applied Mathematics Letters ◽

10.1016/j.aml.2020.106519 ◽

2020 ◽

Vol 109 ◽

pp. 106519

Author(s):

Bingquan Ji ◽

Luming Zhang

Keyword(s):

Spectral Method ◽

Fourth Order ◽

Gordon Equation ◽

Exponential Wave Integrator ◽

Klein Gordon ◽

Pseudo Spectral Method ◽

Pseudo Spectral ◽

Klein Gordon Equation

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