Overlapping domain decomposition method for singularly perturbed third order reaction-diffusion problems

In this paper, we present an analysis of overlapping Schwarz method for singularly perturbed third order reaction-diffusion problems. The Schwarz method invokes two fine mesh subdomains and one coarse mesh subdomain. On each subdomain we use a standard finite difference operator with a uniform mesh....

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Published inAin Shams Engineering Journal Vol. 9; no. 4; pp. 2171 - 2181
Main Authors Christy Roja, J., Tamilselvan, A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2018
Elsevier
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ISSN2090-4479
2090-4495
2090-4495
DOI10.1016/j.asej.2016.09.018

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Abstract In this paper, we present an analysis of overlapping Schwarz method for singularly perturbed third order reaction-diffusion problems. The Schwarz method invokes two fine mesh subdomains and one coarse mesh subdomain. On each subdomain we use a standard finite difference operator with a uniform mesh. The numerical approximations generated from the method are shown to be almost second order uniformly convergent. Furthermore we show that for small ε, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results.
AbstractList In this paper, we present an analysis of overlapping Schwarz method for singularly perturbed third order reaction-diffusion problems. The Schwarz method invokes two fine mesh subdomains and one coarse mesh subdomain. On each subdomain we use a standard finite difference operator with a uniform mesh. The numerical approximations generated from the method are shown to be almost second order uniformly convergent. Furthermore we show that for small ε, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results.
In this paper, we present an analysis of overlapping Schwarz method for singularly perturbed third order reaction-diffusion problems. The Schwarz method invokes two fine mesh subdomains and one coarse mesh subdomain. On each subdomain we use a standard finite difference operator with a uniform mesh. The numerical approximations generated from the method are shown to be almost second order uniformly convergent. Furthermore we show that for small ε, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. Keywords: Singularly perturbed problems, Third order ordinary differential equation, Reaction-diffusion equations, Schwarz method, Subject classification: AMS 65L11, CR G1.7
Author Christy Roja, J.
Tamilselvan, A.
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10.1080/00207160601177200
10.1016/S0168-9274(99)00140-3
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Issue 4
Keywords Singularly perturbed problems
AMS 65L11
Reaction-diffusion equations
Third order ordinary differential equation
CR G1.7
Schwarz method
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Snippet In this paper, we present an analysis of overlapping Schwarz method for singularly perturbed third order reaction-diffusion problems. The Schwarz method...
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SubjectTerms Reaction-diffusion equations
Schwarz method
Singularly perturbed problems
Third order ordinary differential equation
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Title Overlapping domain decomposition method for singularly perturbed third order reaction-diffusion problems
URI https://dx.doi.org/10.1016/j.asej.2016.09.018
https://doi.org/10.1016/j.asej.2016.09.018
https://doaj.org/article/ef744cf74abb4ed7a818ee2e03bece26
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