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 in | Ain Shams Engineering Journal Vol. 9; no. 4; pp. 2171 - 2181 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.12.2018
Elsevier |
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| Online Access | Get full text |
| ISSN | 2090-4479 2090-4495 2090-4495 |
| DOI | 10.1016/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. |
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| 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. |
| Author_xml | – sequence: 1 givenname: J. surname: Christy Roja fullname: Christy Roja, J. email: jchristyrojaa@gmail.com organization: Department of Mathematics, St. Joseph’s College (Autonomous), Tiruchirappalli 620 002, Tamil Nadu, India – sequence: 2 givenname: A. surname: Tamilselvan fullname: Tamilselvan, A. email: mathats@bdu.ac.in organization: Department of Mathematics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India |
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| Cites_doi | 10.1006/jmaa.1999.6497 10.1016/j.cam.2008.12.009 10.1016/0022-0396(90)90099-B 10.1016/0362-546X(94)90143-0 10.1016/j.cam.2014.12.018 10.1016/0022-247X(88)90412-X 10.1080/00207160211284 10.1007/s00607-003-0009-3 10.1137/0143065 10.1016/S0377-0427(99)00380-5 10.1016/S0898-1221(02)00183-9 10.1080/00207160601177200 10.1016/S0168-9274(99)00140-3 10.1016/j.cam.2011.01.047 |
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| Keywords | Singularly perturbed problems AMS 65L11 Reaction-diffusion equations Third order ordinary differential equation CR G1.7 Schwarz method |
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| SubjectTerms | Reaction-diffusion equations Schwarz method Singularly perturbed problems Third order ordinary differential equation |
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