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Volume 28, Issue 6
The Finite Difference Method for Dissipative Klein-Gordon-Schrödinger Equations in Three Space Dimensions

Fayong Zhang & Bo Han

DOI: 10.4208/jcm.1004-m3191

J. Comp. Math., 28 (2010), pp. 879-900.

Published online: 2010-12

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  • Abstract

A fully discrete finite difference scheme for dissipative Klein-Gordon-Schrödinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding theorems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in $H^2\times H^2\times H^1$ over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

  • Keywords

Dissipative Klein–Gordon–Schrödinger equations, Finite difference method, Error bounds, Maximal attractor.

  • AMS Subject Headings

65M06, 35Q55, 65P99.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-879, author = {Fayong Zhang and Bo Han}, title = {The Finite Difference Method for Dissipative Klein-Gordon-Schrödinger Equations in Three Space Dimensions}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {6}, pages = {879--900}, abstract = {

A fully discrete finite difference scheme for dissipative Klein-Gordon-Schrödinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding theorems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in $H^2\times H^2\times H^1$ over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1004-m3191}, url = {http://global-sci.org/intro/article_detail/jcm/8556.html} }
TY - JOUR T1 - The Finite Difference Method for Dissipative Klein-Gordon-Schrödinger Equations in Three Space Dimensions AU - Fayong Zhang & Bo Han JO - Journal of Computational Mathematics VL - 6 SP - 879 EP - 900 PY - 2010 DA - 2010/12 SN - 28 DO - http://doi.org/10.4208/jcm.1004-m3191 UR - https://global-sci.org/intro/article_detail/jcm/8556.html KW - Dissipative Klein–Gordon–Schrödinger equations, Finite difference method, Error bounds, Maximal attractor. AB -

A fully discrete finite difference scheme for dissipative Klein-Gordon-Schrödinger equations in three space dimensions is analyzed. On the basis of a series of the time-uniform priori estimates of the difference solutions and discrete version of Sobolev embedding theorems, the stability of the difference scheme and the error bounds of optimal order for the difference solutions are obtained in $H^2\times H^2\times H^1$ over a finite time interval. Moreover, the existence of a maximal attractor is proved for a discrete dynamical system associated with the fully discrete finite difference scheme.

Fayong Zhang and Bo Han. (2010). The Finite Difference Method for Dissipative Klein-Gordon-Schrödinger Equations in Three Space Dimensions. Journal of Computational Mathematics. 28 (6). 879-900. doi:10.4208/jcm.1004-m3191
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