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Volume 25, Issue 5
Incremental Unknowns for the Heat Equation with Time-Dependent Coefficients: Semi-Implicit $\theta$-Schemes and Their Stability

Yu-Jiang Wu & Ai-Li Yang

J. Comp. Math., 25 (2007), pp. 573-582.

Published online: 2007-10

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  • Abstract

Based on the finite difference discretization of partial differential equations, we propose a kind of semi-implicit $\theta$-schemes of incremental unknowns type for the heat equation with time-dependent coefficients. The stability of the new schemes is carefully studied. Some new types of conditions give better stability when $\theta$ is closed to $1/2$ even if we have variable coefficients.

  • Keywords

Incremental unknowns, Semi-implicit schemes, $θ$-Schemes, Stability.

  • AMS Subject Headings

65M06, 35K05, 65M12, 65P99.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-573, author = {Yu-Jiang Wu and Ai-Li Yang}, title = {Incremental Unknowns for the Heat Equation with Time-Dependent Coefficients: Semi-Implicit $\theta$-Schemes and Their Stability}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {5}, pages = {573--582}, abstract = {

Based on the finite difference discretization of partial differential equations, we propose a kind of semi-implicit $\theta$-schemes of incremental unknowns type for the heat equation with time-dependent coefficients. The stability of the new schemes is carefully studied. Some new types of conditions give better stability when $\theta$ is closed to $1/2$ even if we have variable coefficients.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8714.html} }
TY - JOUR T1 - Incremental Unknowns for the Heat Equation with Time-Dependent Coefficients: Semi-Implicit $\theta$-Schemes and Their Stability AU - Yu-Jiang Wu & Ai-Li Yang JO - Journal of Computational Mathematics VL - 5 SP - 573 EP - 582 PY - 2007 DA - 2007/10 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8714.html KW - Incremental unknowns, Semi-implicit schemes, $θ$-Schemes, Stability. AB -

Based on the finite difference discretization of partial differential equations, we propose a kind of semi-implicit $\theta$-schemes of incremental unknowns type for the heat equation with time-dependent coefficients. The stability of the new schemes is carefully studied. Some new types of conditions give better stability when $\theta$ is closed to $1/2$ even if we have variable coefficients.

Yu-Jiang Wu and Ai-Li Yang. (2007). Incremental Unknowns for the Heat Equation with Time-Dependent Coefficients: Semi-Implicit $\theta$-Schemes and Their Stability. Journal of Computational Mathematics. 25 (5). 573-582. doi:
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