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Volume 21, Issue 2
AD Galerkin Analysis for Nonlinear Pseudo-Hyperbolic Equations

Xia Cui

J. Comp. Math., 21 (2003), pp. 125-134.

Published online: 2003-04

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  • Abstract

AD (Alternating direction) Galerkin schemes for $d$-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized, and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations, difficulty coming from non-linearity is treated, and optimal $H^1$ and $L^2$ convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis.

  • Keywords

nonlinear, pseudo-hyperbolic equation, alternating direction, numerical analysis.

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  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-21-125, author = { Xia Cui }, title = {AD Galerkin Analysis for Nonlinear Pseudo-Hyperbolic Equations}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {2}, pages = {125--134}, abstract = {

AD (Alternating direction) Galerkin schemes for $d$-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized, and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations, difficulty coming from non-linearity is treated, and optimal $H^1$ and $L^2$ convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8875.html} }
TY - JOUR T1 - AD Galerkin Analysis for Nonlinear Pseudo-Hyperbolic Equations AU - Xia Cui JO - Journal of Computational Mathematics VL - 2 SP - 125 EP - 134 PY - 2003 DA - 2003/04 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8875.html KW - nonlinear, pseudo-hyperbolic equation, alternating direction, numerical analysis. AB -

AD (Alternating direction) Galerkin schemes for $d$-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized, and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations, difficulty coming from non-linearity is treated, and optimal $H^1$ and $L^2$ convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis.

Xia Cui . (2003). AD Galerkin Analysis for Nonlinear Pseudo-Hyperbolic Equations. Journal of Computational Mathematics. 21 (2). 125-134. doi:
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