Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems

In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand...

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Published inMathematical modelling and analysis Vol. 26; no. 1; pp. 116 - 134
Main Authors Abbasbandy, Saeid, Sahihi, Hussein, Allahviranloo, Tofigh
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 01.01.2021
Subjects
Analysis
Boundary layer
boundary layer behavior
Boundary layers
Convection
error analysis
Kernels
Methods
reproducing kernel method
singularly perturbed parabolic problems
boundary layer behavior
singularly perturbed parabolic problems
error analysis
reproducing kernel method
Online AccessGet full text
ISSN1392-6292
1648-3510
DOI10.3846/mma.2021.12057

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Abstract In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved.
AbstractList In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved.
In the present paper, reproducing kernel method (RKM) is introduced, which is employed to solve singularly perturbed convection-diffusion parabolic problems (SPCDPPs). It is noteworthy to mention that regarding very serve singularities, there are regular boundary layers in SPCDPPs. On the other hand, getting a reliable approximate solution could be difficult due to the layer behavior of SPCDPPs. The strategy developed in our method is dividing the problem region into two regions, so that one of them would contain a boundary layer behavior. For more illustrations of the method, certain linear and nonlinear SPCDPP are solved. Keywords: reproducing kernel method, singularly perturbed parabolic problems, error analysis, boundary layer behavior. AMS Subject Classification: 35K20; 35K67; 35K55.
Audience Academic
Author Allahviranloo, Tofigh
Sahihi, Hussein
Abbasbandy, Saeid
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  surname: Allahviranloo
  fullname: Allahviranloo, Tofigh
  organization: Faculty of Engineering and Natural Sciences, Bahcesehir University, 34353 Istanbul, Turkey
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Cites_doi 10.1007/s40314-019-0979-1
10.1063/1.5084035
10.1007/BF01398914
10.1016/S0377-0427(02)00861-0
10.1016/j.aml.2013.05.006
10.1016/j.cam.2016.06.029
10.1080/16583655.2019.1651988
10.3846/13926292.2015.1111953
10.1002/num.22079
10.1016/j.camwa.2010.11.019
10.1016/j.apm.2015.01.021
10.1007/s40314-018-0672-9
10.1016/j.cam.2017.05.025
10.1016/j.apnum.2019.12.008
10.1016/j.cpc.2014.04.004
10.1016/j.cam.2016.01.008
10.1080/00207160802047640
10.1002/mma.5950
10.1016/j.amc.2015.05.117
10.3390/math8030360
10.1007/978-3-7091-6961-2
10.1016/j.chaos.2019.06.011
10.1016/j.cam.2014.06.016
10.1007/978-3-662-09017-6
10.1016/j.chaos.2018.07.032
10.1016/j.aml.2014.05.014
10.1007/s40819-019-0714-z
10.1093/oso/9780195108088.001.0001
10.1137/1.9780898719130
10.1016/B978-0-444-50616-0.50018-X
10.1016/j.cam.2008.10.007
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References key-10.3846/mma.2021.12057-2
key-10.3846/mma.2021.12057-15
key-10.3846/mma.2021.12057-1
key-10.3846/mma.2021.12057-14
key-10.3846/mma.2021.12057-4
key-10.3846/mma.2021.12057-17
key-10.3846/mma.2021.12057-3
key-10.3846/mma.2021.12057-16
key-10.3846/mma.2021.12057-6
key-10.3846/mma.2021.12057-11
key-10.3846/mma.2021.12057-33
key-10.3846/mma.2021.12057-5
key-10.3846/mma.2021.12057-10
key-10.3846/mma.2021.12057-32
key-10.3846/mma.2021.12057-8
key-10.3846/mma.2021.12057-13
key-10.3846/mma.2021.12057-7
key-10.3846/mma.2021.12057-12
key-10.3846/mma.2021.12057-34
key-10.3846/mma.2021.12057-31
key-10.3846/mma.2021.12057-30
key-10.3846/mma.2021.12057-29
key-10.3846/mma.2021.12057-26
key-10.3846/mma.2021.12057-25
key-10.3846/mma.2021.12057-28
key-10.3846/mma.2021.12057-27
key-10.3846/mma.2021.12057-22
key-10.3846/mma.2021.12057-21
key-10.3846/mma.2021.12057-24
key-10.3846/mma.2021.12057-23
key-10.3846/mma.2021.12057-20
key-10.3846/mma.2021.12057-9
key-10.3846/mma.2021.12057-19
key-10.3846/mma.2021.12057-18
References_xml – ident: key-10.3846/mma.2021.12057-29
  doi: 10.1007/s40314-019-0979-1
– ident: key-10.3846/mma.2021.12057-3
  doi: 10.1063/1.5084035
– ident: key-10.3846/mma.2021.12057-31
  doi: 10.1007/BF01398914
– ident: key-10.3846/mma.2021.12057-10
  doi: 10.1016/S0377-0427(02)00861-0
– ident: key-10.3846/mma.2021.12057-14
  doi: 10.1016/j.aml.2013.05.006
– ident: key-10.3846/mma.2021.12057-26
  doi: 10.1016/j.cam.2016.06.029
– ident: key-10.3846/mma.2021.12057-2
  doi: 10.1080/16583655.2019.1651988
– ident: key-10.3846/mma.2021.12057-6
  doi: 10.3846/13926292.2015.1111953
– ident: key-10.3846/mma.2021.12057-13
  doi: 10.1002/num.22079
– ident: key-10.3846/mma.2021.12057-34
  doi: 10.1016/j.camwa.2010.11.019
– ident: key-10.3846/mma.2021.12057-16
  doi: 10.1016/j.apm.2015.01.021
– ident: key-10.3846/mma.2021.12057-27
  doi: 10.1007/s40314-018-0672-9
– ident: key-10.3846/mma.2021.12057-11
– ident: key-10.3846/mma.2021.12057-7
  doi: 10.1016/j.cam.2017.05.025
– ident: key-10.3846/mma.2021.12057-25
  doi: 10.1016/j.apnum.2019.12.008
– ident: key-10.3846/mma.2021.12057-17
  doi: 10.1016/j.cpc.2014.04.004
– ident: key-10.3846/mma.2021.12057-8
  doi: 10.1016/j.cam.2016.01.008
– ident: key-10.3846/mma.2021.12057-32
  doi: 10.1080/00207160802047640
– ident: key-10.3846/mma.2021.12057-22
– ident: key-10.3846/mma.2021.12057-24
– ident: key-10.3846/mma.2021.12057-4
  doi: 10.1002/mma.5950
– ident: key-10.3846/mma.2021.12057-21
  doi: 10.1016/j.amc.2015.05.117
– ident: key-10.3846/mma.2021.12057-9
  doi: 10.3390/math8030360
– ident: key-10.3846/mma.2021.12057-23
  doi: 10.1007/978-3-7091-6961-2
– ident: key-10.3846/mma.2021.12057-5
  doi: 10.1016/j.chaos.2019.06.011
– ident: key-10.3846/mma.2021.12057-19
  doi: 10.1016/j.cam.2014.06.016
– ident: key-10.3846/mma.2021.12057-18
  doi: 10.1007/978-3-662-09017-6
– ident: key-10.3846/mma.2021.12057-1
  doi: 10.1016/j.chaos.2018.07.032
– ident: key-10.3846/mma.2021.12057-15
  doi: 10.1016/j.aml.2014.05.014
– ident: key-10.3846/mma.2021.12057-28
  doi: 10.1007/s40819-019-0714-z
– ident: key-10.3846/mma.2021.12057-30
  doi: 10.1093/oso/9780195108088.001.0001
– ident: key-10.3846/mma.2021.12057-20
  doi: 10.1137/1.9780898719130
– ident: key-10.3846/mma.2021.12057-12
  doi: 10.1016/B978-0-444-50616-0.50018-X
– ident: key-10.3846/mma.2021.12057-33
  doi: 10.1016/j.cam.2008.10.007
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SubjectTerms Analysis
Boundary layer
boundary layer behavior
Boundary layers
Convection
error analysis
Kernels
Methods
reproducing kernel method
singularly perturbed parabolic problems
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Title Implementing reproducing kernel method to solve singularly perturbed convection-diffusion parabolic problems
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