Volume 15, Issue 3
Convergence of a Conservative Difference Scheme for the Zakharov Equations in Two Dimensions
DOI:

J. Comp. Math., 15 (1997), pp. 219-232

Published online: 1997-06

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• Abstract

A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in $L_2$ norm, the convergence of the difference solution is proved in order $O(h^2+r^2)$. In the proof, a new skill is used to deal with the term of difference quotient $(e_{j,k}^n)t$. This is necessary, since there is no estimate of $E(x,y,t)$ in $L_\infty$ norm.

• Keywords

@Article{JCM-15-219, author = {}, title = {Convergence of a Conservative Difference Scheme for the Zakharov Equations in Two Dimensions}, journal = {Journal of Computational Mathematics}, year = {1997}, volume = {15}, number = {3}, pages = {219--232}, abstract = { A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in $L_2$ norm, the convergence of the difference solution is proved in order $O(h^2+r^2)$. In the proof, a new skill is used to deal with the term of difference quotient $(e_{j,k}^n)t$. This is necessary, since there is no estimate of $E(x,y,t)$ in $L_\infty$ norm. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9201.html} }
TY - JOUR T1 - Convergence of a Conservative Difference Scheme for the Zakharov Equations in Two Dimensions JO - Journal of Computational Mathematics VL - 3 SP - 219 EP - 232 PY - 1997 DA - 1997/06 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9201.html KW - AB - A conservative difference scheme is presented for the initial-boundary-value problem of a generalized Zakharov equations. On the basis of a prior estimates in $L_2$ norm, the convergence of the difference solution is proved in order $O(h^2+r^2)$. In the proof, a new skill is used to deal with the term of difference quotient $(e_{j,k}^n)t$. This is necessary, since there is no estimate of $E(x,y,t)$ in $L_\infty$ norm.