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Volume 22, Issue 1
A Practical Parallel Difference Scheme for Parabolic Equations

Jiaquan Gao

J. Comp. Math., 22 (2004), pp. 55-60.

Published online: 2004-02

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  • Abstract

A practical parallel difference scheme for parabolic equations is constructed as follows: to decompose the domain Ω into some overlapping subdomains, take flux of the last time layer as Neumann boundary conditions for the time layer on inner boundary points of subdomains, solve it with the fully implicit scheme on each subdomain, then take correspondent values of its neighbor subdomains as its values for inner boundary points of each subdomain and mean of its neighbor subdomain and itself at overlapping points. The scheme is unconditionally convergent. Though its truncation error is $O(h+\tau)$the convergent order for the solution can be improved to $O(h^2+\tau)$.

  • Keywords

Parallel difference scheme, Parabolic equation, Segment, Explicit-implicit.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-55, author = {Gao , Jiaquan}, title = {A Practical Parallel Difference Scheme for Parabolic Equations}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {1}, pages = {55--60}, abstract = {

A practical parallel difference scheme for parabolic equations is constructed as follows: to decompose the domain Ω into some overlapping subdomains, take flux of the last time layer as Neumann boundary conditions for the time layer on inner boundary points of subdomains, solve it with the fully implicit scheme on each subdomain, then take correspondent values of its neighbor subdomains as its values for inner boundary points of each subdomain and mean of its neighbor subdomain and itself at overlapping points. The scheme is unconditionally convergent. Though its truncation error is $O(h+\tau)$the convergent order for the solution can be improved to $O(h^2+\tau)$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10333.html} }
TY - JOUR T1 - A Practical Parallel Difference Scheme for Parabolic Equations AU - Gao , Jiaquan JO - Journal of Computational Mathematics VL - 1 SP - 55 EP - 60 PY - 2004 DA - 2004/02 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10333.html KW - Parallel difference scheme, Parabolic equation, Segment, Explicit-implicit. AB -

A practical parallel difference scheme for parabolic equations is constructed as follows: to decompose the domain Ω into some overlapping subdomains, take flux of the last time layer as Neumann boundary conditions for the time layer on inner boundary points of subdomains, solve it with the fully implicit scheme on each subdomain, then take correspondent values of its neighbor subdomains as its values for inner boundary points of each subdomain and mean of its neighbor subdomain and itself at overlapping points. The scheme is unconditionally convergent. Though its truncation error is $O(h+\tau)$the convergent order for the solution can be improved to $O(h^2+\tau)$.

Gao , Jiaquan. (2004). A Practical Parallel Difference Scheme for Parabolic Equations. Journal of Computational Mathematics. 22 (1). 55-60. doi:
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