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Volume 1, Issue 2
Convergence and Stability of Explicit/Implicit Schemes for Parabolic Equations with Discontinuous Coefficients

Shaohong Zhu, Guangwei Yuan & Weiwei Sun

Int. J. Numer. Anal. Mod., 1 (2004), pp. 131-146.

Published online: 2004-01

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  • Abstract

In this paper an explicit/implicit schemes for parabolic equations with discontinuous coefficients is analyzed. We show that the error of the solution in $L^∞$ norm and the error of the discrete flux in $L^2$ norm are in order $O(\tau + h^2)$ and $O(\tau + h^{\frac{3}{2}})$, respectively and the scheme is stable under some weaker conditions, while the difference scheme has the truncation error $O(1)$ at the neighboring points of the discontinuity of the coefficient. Numerical experiments, which are given for both linear and nonlinear problems, show that our theoretical estimates are optimal in some sense. The comparison with some classical scheme is presented.

  • Keywords

Domain decomposition, parabolic equations, discontinuous coefficient, parallel difference schemes, convergence.

  • AMS Subject Headings

65M60, 65P05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-1-131, author = {Zhu , ShaohongYuan , Guangwei and Sun , Weiwei}, title = {Convergence and Stability of Explicit/Implicit Schemes for Parabolic Equations with Discontinuous Coefficients}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2004}, volume = {1}, number = {2}, pages = {131--146}, abstract = {

In this paper an explicit/implicit schemes for parabolic equations with discontinuous coefficients is analyzed. We show that the error of the solution in $L^∞$ norm and the error of the discrete flux in $L^2$ norm are in order $O(\tau + h^2)$ and $O(\tau + h^{\frac{3}{2}})$, respectively and the scheme is stable under some weaker conditions, while the difference scheme has the truncation error $O(1)$ at the neighboring points of the discontinuity of the coefficient. Numerical experiments, which are given for both linear and nonlinear problems, show that our theoretical estimates are optimal in some sense. The comparison with some classical scheme is presented.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/970.html} }
TY - JOUR T1 - Convergence and Stability of Explicit/Implicit Schemes for Parabolic Equations with Discontinuous Coefficients AU - Zhu , Shaohong AU - Yuan , Guangwei AU - Sun , Weiwei JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 131 EP - 146 PY - 2004 DA - 2004/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/970.html KW - Domain decomposition, parabolic equations, discontinuous coefficient, parallel difference schemes, convergence. AB -

In this paper an explicit/implicit schemes for parabolic equations with discontinuous coefficients is analyzed. We show that the error of the solution in $L^∞$ norm and the error of the discrete flux in $L^2$ norm are in order $O(\tau + h^2)$ and $O(\tau + h^{\frac{3}{2}})$, respectively and the scheme is stable under some weaker conditions, while the difference scheme has the truncation error $O(1)$ at the neighboring points of the discontinuity of the coefficient. Numerical experiments, which are given for both linear and nonlinear problems, show that our theoretical estimates are optimal in some sense. The comparison with some classical scheme is presented.

Shaohong Zhu, Guangwei Yuan & Weiwei Sun. (1970). Convergence and Stability of Explicit/Implicit Schemes for Parabolic Equations with Discontinuous Coefficients. International Journal of Numerical Analysis and Modeling. 1 (2). 131-146. doi:
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