A uniformly convergent numerical scheme for two parameters singularly perturbed parabolic convection–diffusion problems with a large temporal lag
In the present paper, an exponentially fitted numerical scheme is constructed and analyzed for solving singularly perturbed two-parameter parabolic problems with large temporal lag. The problem is discretized by the Crank–Nicolson scheme and the exponentially fitted cubic spline scheme for temporal...
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| Published in | Results in applied mathematics Vol. 16; p. 100338 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.11.2022
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2590-0374 2590-0374 |
| DOI | 10.1016/j.rinam.2022.100338 |
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| Abstract | In the present paper, an exponentially fitted numerical scheme is constructed and analyzed for solving singularly perturbed two-parameter parabolic problems with large temporal lag. The problem is discretized by the Crank–Nicolson scheme and the exponentially fitted cubic spline scheme for temporal and spatial derivatives respectively. The resulting scheme is shown to be second-order convergent both in the temporal and spatial directions. Two numerical examples are presented to support the theoretical analysis developed in this article. The present numerical results are compared with the results in the literature which confirm the efficiency of the present scheme. |
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| AbstractList | In the present paper, an exponentially fitted numerical scheme is constructed and analyzed for solving singularly perturbed two-parameter parabolic problems with large temporal lag. The problem is discretized by the Crank–Nicolson scheme and the exponentially fitted cubic spline scheme for temporal and spatial derivatives respectively. The resulting scheme is shown to be second-order convergent both in the temporal and spatial directions. Two numerical examples are presented to support the theoretical analysis developed in this article. The present numerical results are compared with the results in the literature which confirm the efficiency of the present scheme. |
| ArticleNumber | 100338 |
| Author | Negero, Naol Tufa |
| Author_xml | – sequence: 1 givenname: Naol Tufa orcidid: 0000-0003-1593-735X surname: Negero fullname: Negero, Naol Tufa email: natitfa@gmail.com organization: Department of Mathematics, Wollega University, Nekemte, Ethiopia |
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| CitedBy_id | crossref_primary_10_3389_fams_2023_1260651 crossref_primary_10_1016_j_rinam_2023_100405 crossref_primary_10_1016_j_padiff_2023_100518 crossref_primary_10_1186_s13104_023_06457_1 crossref_primary_10_1016_j_rinp_2023_106724 crossref_primary_10_11121_ijocta_1414 crossref_primary_10_3389_fams_2023_1255672 crossref_primary_10_1016_j_padiff_2023_100546 crossref_primary_10_1016_j_padiff_2023_100530 crossref_primary_10_1016_j_rinam_2023_100361 |
| Cites_doi | 10.1080/00207160.2018.1432856 10.1016/j.apnum.2005.08.002 10.1007/s40819-019-0672-5 10.1016/S0304-0208(08)70556-5 10.1016/j.cam.2015.10.031 10.1007/s40995-021-01258-2 10.1016/S0898-1221(00)00192-9 10.1080/25742558.2020.1829277 10.1080/10236190701817383 10.1080/00207160.2016.1154948 10.1080/00207160.2014.928701 10.1115/1.1568121 10.1016/0022-247X(83)90094-X 10.1016/j.cam.2015.07.011 10.1016/j.rinam.2021.100174 10.1155/2021/6641236 10.1002/num.22544 10.1016/j.cam.2006.05.032 10.1007/s10543-015-0559-8 10.1007/s40314-020-01278-5 10.1016/S0898-1221(97)00279-4 10.1016/j.camwa.2013.06.025 10.1016/S0045-7825(98)00243-6 10.1016/j.aej.2020.03.042 10.1080/01442359209353268 10.1080/15502287.2021.1948148 10.1007/s12190-019-01313-7 10.1016/j.rinam.2022.100324 |
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| Keywords | Parabolic convection–diffusion problem Two small parameters Exponentially fitted cubic spline method Time delay Singular perturbation |
| Language | English |
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| References | DiPrima (b9) 1968 Ansari, Bakr, Shishkin (b18) 2007; 205 Govindarao, Mohapatra, Sahu (b40) 2019; 5 Mbroh, Noutchie, Massoukou (b21) 2020; 59 Kumar, Kanth (b22) 2020; 39 Li, Navon (b16) 1998; 35 Woldaregay, Aniley, Duressa (b27) 2021; 2021 Kumar (b28) 2021; 37 Kumar, Kumar (b41) 2020; 39 Negero, Duressa (b26) 2022; 10 Li, Navon (b15) 1999; 171 Adomian, Rach (b4) 1983; 91 Bullo, Degla, Duressa (b39) 2022; 23 Epstein (b5) 1992; 11 Hale, Lunel (b6) 2013 Clavero, Gracia, Shishkin, Shishkina (b37) 2017; 318 Das, Mehrmann (b36) 2016; 56 Wondimu Gelu, Duressa (b12) 2022; 9 O’Malley RE. Introduction to singular perturbations. Tech. rep., 1974. Das, Natesan (b19) 2015; 271 Govindarao, Mohapatra, Das (b23) 2020; 63 Gelu, Duressa (b14) 2022; 15 Negero, Duressa (b24) 2022; 46 Brdar, Zarin (b34) 2016; 292 Jha, Kadalbajoo (b35) 2015; 92 GELU, DURESSA (b17) 2022; 40 Wu (b7) 2012 Negero, Duressa (b29) 2021; 11 O’Malley (b30) 1967; 16 Patidar (b32) 2008; 14 Gelu, Duressa (b25) 2021 Asl, Ulsoy (b2) 2003; 125 Li, Chen (b13) 2008; 1 Tikhonov, Samarskii (b1) 2013 Li (b11) 2000; 40 Gupta, Kadalbajoo, Dubey (b10) 2019; 96 Gowrisankar, Natesan (b20) 2017; 94 Mekonnen, Duressa (b38) 2020; 7 Van Harten, Schumacher (b3) 1978 Wu, Zhang, Yuan (b33) 2013; 66 Gracia, O’Riordan, Pickett (b31) 2006; 56 Mbroh (10.1016/j.rinam.2022.100338_b21) 2020; 59 Negero (10.1016/j.rinam.2022.100338_b29) 2021; 11 10.1016/j.rinam.2022.100338_b8 Kumar (10.1016/j.rinam.2022.100338_b28) 2021; 37 Wondimu Gelu (10.1016/j.rinam.2022.100338_b12) 2022; 9 GELU (10.1016/j.rinam.2022.100338_b17) 2022; 40 Govindarao (10.1016/j.rinam.2022.100338_b23) 2020; 63 Hale (10.1016/j.rinam.2022.100338_b6) 2013 Bullo (10.1016/j.rinam.2022.100338_b39) 2022; 23 Gowrisankar (10.1016/j.rinam.2022.100338_b20) 2017; 94 Patidar (10.1016/j.rinam.2022.100338_b32) 2008; 14 Das (10.1016/j.rinam.2022.100338_b36) 2016; 56 Li (10.1016/j.rinam.2022.100338_b13) 2008; 1 Gupta (10.1016/j.rinam.2022.100338_b10) 2019; 96 O’Malley (10.1016/j.rinam.2022.100338_b30) 1967; 16 Das (10.1016/j.rinam.2022.100338_b19) 2015; 271 Woldaregay (10.1016/j.rinam.2022.100338_b27) 2021; 2021 Govindarao (10.1016/j.rinam.2022.100338_b40) 2019; 5 Gelu (10.1016/j.rinam.2022.100338_b14) 2022; 15 Wu (10.1016/j.rinam.2022.100338_b33) 2013; 66 Li (10.1016/j.rinam.2022.100338_b16) 1998; 35 Negero (10.1016/j.rinam.2022.100338_b24) 2022; 46 Clavero (10.1016/j.rinam.2022.100338_b37) 2017; 318 Ansari (10.1016/j.rinam.2022.100338_b18) 2007; 205 Brdar (10.1016/j.rinam.2022.100338_b34) 2016; 292 Tikhonov (10.1016/j.rinam.2022.100338_b1) 2013 Negero (10.1016/j.rinam.2022.100338_b26) 2022; 10 Gracia (10.1016/j.rinam.2022.100338_b31) 2006; 56 Gelu (10.1016/j.rinam.2022.100338_b25) 2021 Wu (10.1016/j.rinam.2022.100338_b7) 2012 Kumar (10.1016/j.rinam.2022.100338_b41) 2020; 39 Epstein (10.1016/j.rinam.2022.100338_b5) 1992; 11 Mekonnen (10.1016/j.rinam.2022.100338_b38) 2020; 7 Li (10.1016/j.rinam.2022.100338_b11) 2000; 40 DiPrima (10.1016/j.rinam.2022.100338_b9) 1968 Asl (10.1016/j.rinam.2022.100338_b2) 2003; 125 Li (10.1016/j.rinam.2022.100338_b15) 1999; 171 Kumar (10.1016/j.rinam.2022.100338_b22) 2020; 39 Adomian (10.1016/j.rinam.2022.100338_b4) 1983; 91 Van Harten (10.1016/j.rinam.2022.100338_b3) 1978 Jha (10.1016/j.rinam.2022.100338_b35) 2015; 92 |
| References_xml | – volume: 94 start-page: 902 year: 2017 end-page: 921 ident: b20 article-title: -Uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations publication-title: Int J Comput Math – volume: 7 year: 2020 ident: b38 article-title: Computational method for singularly perturbed two-parameter parabolic convection-diffusion problems publication-title: Cogent Math Stat – volume: 59 start-page: 2543 year: 2020 end-page: 2554 ident: b21 article-title: A robust method of lines solution for singularly perturbed delay parabolic problem publication-title: Alexandria Eng J – year: 2021 ident: b25 article-title: A uniformly convergent collocation method for singularly perturbed delay parabolic reaction-diffusion problem publication-title: Abstract and applied analysis, Vol. 2021 – year: 2013 ident: b1 article-title: Equations of mathematical physics – volume: 40 start-page: 25 year: 2022 end-page: 45 ident: b17 article-title: Computational method for singularly perturbed parabolic reaction-diffusion equations with Robin boundary conditions publication-title: J Appl Math Inf – volume: 5 start-page: 1 year: 2019 end-page: 9 ident: b40 article-title: Uniformly convergent numerical method for singularly perturbed two parameter time delay parabolic problem publication-title: Int J Appl Comput Math – volume: 271 start-page: 168 year: 2015 end-page: 186 ident: b19 article-title: Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh publication-title: Appl Math Comput – volume: 11 year: 2021 ident: b29 article-title: A method of line with improved accuracy for singularly perturbed parabolic convection–diffusion problems with large temporal lag publication-title: Results Appl Math – year: 2013 ident: b6 article-title: Introduction to functional differential equations, Vol. 99 – year: 1968 ident: b9 article-title: Asymptotic methods for an infinitely long slider squeeze-film bearing – volume: 96 start-page: 474 year: 2019 end-page: 499 ident: b10 article-title: A parameter-uniform higher order finite difference scheme for singularly perturbed time-dependent parabolic problem with two small parameters publication-title: Int J Comput Math – reference: O’Malley RE. Introduction to singular perturbations. Tech. rep., 1974. – volume: 37 start-page: 626 year: 2021 end-page: 642 ident: b28 article-title: A parameter-uniform scheme for the parabolic singularly perturbed problem with a delay in time publication-title: Numer Methods Partial Differential Equations – volume: 15 year: 2022 ident: b14 article-title: Parameter-uniform numerical scheme for singularly perturbed parabolic convection–diffusion Robin type problems with a boundary turning point publication-title: Results Appl Math – volume: 91 start-page: 94 year: 1983 end-page: 101 ident: b4 article-title: Nonlinear stochastic differential delay equations publication-title: J Math Anal Appl – volume: 40 start-page: 735 year: 2000 end-page: 745 ident: b11 article-title: Convergence analysis of finite element methods for singularly perturbed problems publication-title: Comput Math Appl – volume: 14 start-page: 1197 year: 2008 end-page: 1214 ident: b32 article-title: A robust fitted operator finite difference method for a two-parameter singular perturbation problem1 publication-title: J Difference Equ Appl – volume: 10 start-page: 173 year: 2022 end-page: 190 ident: b26 article-title: An efficient numerical approach for singularly perturbed parabolic convection-diffusion problems with large time-lag publication-title: J Math Model – volume: 125 start-page: 215 year: 2003 end-page: 223 ident: b2 article-title: Analysis of a system of linear delay differential equations publication-title: J Dyn Syst Meas Control – volume: 56 start-page: 51 year: 2016 end-page: 76 ident: b36 article-title: Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters publication-title: BIT Numer Math – volume: 23 start-page: 210 year: 2022 end-page: 218 ident: b39 article-title: Parameter-uniform finite difference method for singularly perturbed parabolic problem with two small parameters publication-title: Int J Comput Methods Eng Sci Mech – volume: 205 start-page: 552 year: 2007 end-page: 566 ident: b18 article-title: A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations publication-title: J Comput Appl Math – volume: 9 year: 2022 ident: b12 article-title: A novel numerical approach for singularly perturbed parabolic convection-diffusion problems on layer-adapted meshes publication-title: Res Math – year: 2012 ident: b7 article-title: Theory and applications of partial functional differential equations, Vol. 119 – volume: 2021 year: 2021 ident: b27 article-title: Novel numerical scheme for singularly perturbed time delay convection-diffusion equation publication-title: Adv Math Phys – volume: 35 start-page: 57 year: 1998 end-page: 70 ident: b16 article-title: Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems I: reaction-diffusion type publication-title: Comput Math Appl – volume: 63 start-page: 171 year: 2020 end-page: 195 ident: b23 article-title: A fourth-order numerical scheme for singularly perturbed delay parabolic problem arising in population dynamics publication-title: J Appl Math Comput – volume: 16 start-page: 1143 year: 1967 end-page: 1164 ident: b30 article-title: Two-parameter singular perturbation problems for second-order equations publication-title: J Math Mech – volume: 92 start-page: 1204 year: 2015 end-page: 1221 ident: b35 article-title: A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems publication-title: Int J Comput Math – volume: 39 start-page: 1 year: 2020 end-page: 25 ident: b41 article-title: A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem publication-title: Comput Appl Math – volume: 39 start-page: 1 year: 2020 end-page: 19 ident: b22 article-title: Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline publication-title: Comput Appl Math – volume: 171 start-page: 1 year: 1999 end-page: 23 ident: b15 article-title: Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: higher-order elements publication-title: Comput Methods Appl Mech Engrg – volume: 56 start-page: 962 year: 2006 end-page: 980 ident: b31 article-title: A parameter robust second order numerical method for a singularly perturbed two-parameter problem publication-title: Appl Numer Math – volume: 292 start-page: 307 year: 2016 end-page: 319 ident: b34 article-title: A singularly perturbed problem with two parameters on a Bakhvalov-type mesh publication-title: J Comput Appl Math – volume: 11 start-page: 135 year: 1992 end-page: 160 ident: b5 article-title: Delay effects and differential delay equations in chemical kinetics publication-title: Int Rev Phys Chem – volume: 318 start-page: 634 year: 2017 end-page: 645 ident: b37 article-title: An efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers publication-title: J Comput Appl Math – volume: 66 start-page: 996 year: 2013 end-page: 1009 ident: b33 article-title: A robust adaptive method for singularly perturbed convection–diffusion problem with two small parameters publication-title: Comput Math Appl – start-page: 161 year: 1978 end-page: 179 ident: b3 article-title: On a class of partial functional differential equations arising in feed-back control theory publication-title: North-Holland mathematics studies, Vol. 31 – volume: 1 start-page: 138 year: 2008 end-page: 149 ident: b13 article-title: Uniform convergence analysis for singularly perturbed elliptic problems with parabolic layers publication-title: Numer Math Theory Methods Appl – volume: 46 start-page: 507 year: 2022 end-page: 524 ident: b24 article-title: Uniform convergent solution of singularly perturbed parabolic differential equations with general temporal-lag publication-title: Iran J Sci Technol Trans A Sci – volume: 96 start-page: 474 issue: 3 year: 2019 ident: 10.1016/j.rinam.2022.100338_b10 article-title: A parameter-uniform higher order finite difference scheme for singularly perturbed time-dependent parabolic problem with two small parameters publication-title: Int J Comput Math doi: 10.1080/00207160.2018.1432856 – volume: 56 start-page: 962 issue: 7 year: 2006 ident: 10.1016/j.rinam.2022.100338_b31 article-title: A parameter robust second order numerical method for a singularly perturbed two-parameter problem publication-title: Appl Numer Math doi: 10.1016/j.apnum.2005.08.002 – volume: 10 start-page: 173 issue: 2 year: 2022 ident: 10.1016/j.rinam.2022.100338_b26 article-title: An efficient numerical approach for singularly perturbed parabolic convection-diffusion problems with large time-lag publication-title: J Math Model – volume: 5 start-page: 1 issue: 3 year: 2019 ident: 10.1016/j.rinam.2022.100338_b40 article-title: Uniformly convergent numerical method for singularly perturbed two parameter time delay parabolic problem publication-title: Int J Appl Comput Math doi: 10.1007/s40819-019-0672-5 – year: 2013 ident: 10.1016/j.rinam.2022.100338_b1 – start-page: 161 year: 1978 ident: 10.1016/j.rinam.2022.100338_b3 article-title: On a class of partial functional differential equations arising in feed-back control theory doi: 10.1016/S0304-0208(08)70556-5 – volume: 318 start-page: 634 year: 2017 ident: 10.1016/j.rinam.2022.100338_b37 article-title: An efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers publication-title: J Comput Appl Math doi: 10.1016/j.cam.2015.10.031 – ident: 10.1016/j.rinam.2022.100338_b8 – volume: 46 start-page: 507 issue: 2 year: 2022 ident: 10.1016/j.rinam.2022.100338_b24 article-title: Uniform convergent solution of singularly perturbed parabolic differential equations with general temporal-lag publication-title: Iran J Sci Technol Trans A Sci doi: 10.1007/s40995-021-01258-2 – volume: 40 start-page: 735 issue: 6–7 year: 2000 ident: 10.1016/j.rinam.2022.100338_b11 article-title: Convergence analysis of finite element methods for singularly perturbed problems publication-title: Comput Math Appl doi: 10.1016/S0898-1221(00)00192-9 – volume: 7 issue: 1 year: 2020 ident: 10.1016/j.rinam.2022.100338_b38 article-title: Computational method for singularly perturbed two-parameter parabolic convection-diffusion problems publication-title: Cogent Math Stat doi: 10.1080/25742558.2020.1829277 – volume: 14 start-page: 1197 issue: 12 year: 2008 ident: 10.1016/j.rinam.2022.100338_b32 article-title: A robust fitted operator finite difference method for a two-parameter singular perturbation problem1 publication-title: J Difference Equ Appl doi: 10.1080/10236190701817383 – year: 2013 ident: 10.1016/j.rinam.2022.100338_b6 – volume: 94 start-page: 902 issue: 5 year: 2017 ident: 10.1016/j.rinam.2022.100338_b20 article-title: ɛ-Uniformly convergent numerical scheme for singularly perturbed delay parabolic partial differential equations publication-title: Int J Comput Math doi: 10.1080/00207160.2016.1154948 – volume: 92 start-page: 1204 issue: 6 year: 2015 ident: 10.1016/j.rinam.2022.100338_b35 article-title: A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems publication-title: Int J Comput Math doi: 10.1080/00207160.2014.928701 – volume: 125 start-page: 215 issue: 2 year: 2003 ident: 10.1016/j.rinam.2022.100338_b2 article-title: Analysis of a system of linear delay differential equations publication-title: J Dyn Syst Meas Control doi: 10.1115/1.1568121 – volume: 91 start-page: 94 issue: 1 year: 1983 ident: 10.1016/j.rinam.2022.100338_b4 article-title: Nonlinear stochastic differential delay equations publication-title: J Math Anal Appl doi: 10.1016/0022-247X(83)90094-X – year: 1968 ident: 10.1016/j.rinam.2022.100338_b9 – volume: 16 start-page: 1143 issue: 10 year: 1967 ident: 10.1016/j.rinam.2022.100338_b30 article-title: Two-parameter singular perturbation problems for second-order equations publication-title: J Math Mech – volume: 271 start-page: 168 year: 2015 ident: 10.1016/j.rinam.2022.100338_b19 article-title: Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh publication-title: Appl Math Comput – volume: 40 start-page: 25 issue: 1_2 year: 2022 ident: 10.1016/j.rinam.2022.100338_b17 article-title: Computational method for singularly perturbed parabolic reaction-diffusion equations with Robin boundary conditions publication-title: J Appl Math Inf – volume: 292 start-page: 307 year: 2016 ident: 10.1016/j.rinam.2022.100338_b34 article-title: A singularly perturbed problem with two parameters on a Bakhvalov-type mesh publication-title: J Comput Appl Math doi: 10.1016/j.cam.2015.07.011 – volume: 11 year: 2021 ident: 10.1016/j.rinam.2022.100338_b29 article-title: A method of line with improved accuracy for singularly perturbed parabolic convection–diffusion problems with large temporal lag publication-title: Results Appl Math doi: 10.1016/j.rinam.2021.100174 – volume: 1 start-page: 138 year: 2008 ident: 10.1016/j.rinam.2022.100338_b13 article-title: Uniform convergence analysis for singularly perturbed elliptic problems with parabolic layers publication-title: Numer Math Theory Methods Appl – volume: 2021 year: 2021 ident: 10.1016/j.rinam.2022.100338_b27 article-title: Novel numerical scheme for singularly perturbed time delay convection-diffusion equation publication-title: Adv Math Phys doi: 10.1155/2021/6641236 – volume: 37 start-page: 626 issue: 1 year: 2021 ident: 10.1016/j.rinam.2022.100338_b28 article-title: A parameter-uniform scheme for the parabolic singularly perturbed problem with a delay in time publication-title: Numer Methods Partial Differential Equations doi: 10.1002/num.22544 – volume: 205 start-page: 552 issue: 1 year: 2007 ident: 10.1016/j.rinam.2022.100338_b18 article-title: A parameter-robust finite difference method for singularly perturbed delay parabolic partial differential equations publication-title: J Comput Appl Math doi: 10.1016/j.cam.2006.05.032 – volume: 56 start-page: 51 issue: 1 year: 2016 ident: 10.1016/j.rinam.2022.100338_b36 article-title: Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters publication-title: BIT Numer Math doi: 10.1007/s10543-015-0559-8 – volume: 39 start-page: 1 issue: 3 year: 2020 ident: 10.1016/j.rinam.2022.100338_b22 article-title: Computational study for a class of time-dependent singularly perturbed parabolic partial differential equation through tension spline publication-title: Comput Appl Math doi: 10.1007/s40314-020-01278-5 – volume: 39 start-page: 1 issue: 3 year: 2020 ident: 10.1016/j.rinam.2022.100338_b41 article-title: A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem publication-title: Comput Appl Math – volume: 35 start-page: 57 issue: 3 year: 1998 ident: 10.1016/j.rinam.2022.100338_b16 article-title: Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems I: reaction-diffusion type publication-title: Comput Math Appl doi: 10.1016/S0898-1221(97)00279-4 – volume: 66 start-page: 996 issue: 6 year: 2013 ident: 10.1016/j.rinam.2022.100338_b33 article-title: A robust adaptive method for singularly perturbed convection–diffusion problem with two small parameters publication-title: Comput Math Appl doi: 10.1016/j.camwa.2013.06.025 – volume: 171 start-page: 1 issue: 1–2 year: 1999 ident: 10.1016/j.rinam.2022.100338_b15 article-title: Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: higher-order elements publication-title: Comput Methods Appl Mech Engrg doi: 10.1016/S0045-7825(98)00243-6 – volume: 59 start-page: 2543 issue: 4 year: 2020 ident: 10.1016/j.rinam.2022.100338_b21 article-title: A robust method of lines solution for singularly perturbed delay parabolic problem publication-title: Alexandria Eng J doi: 10.1016/j.aej.2020.03.042 – volume: 11 start-page: 135 issue: 1 year: 1992 ident: 10.1016/j.rinam.2022.100338_b5 article-title: Delay effects and differential delay equations in chemical kinetics publication-title: Int Rev Phys Chem doi: 10.1080/01442359209353268 – volume: 23 start-page: 210 issue: 3 year: 2022 ident: 10.1016/j.rinam.2022.100338_b39 article-title: Parameter-uniform finite difference method for singularly perturbed parabolic problem with two small parameters publication-title: Int J Comput Methods Eng Sci Mech doi: 10.1080/15502287.2021.1948148 – year: 2012 ident: 10.1016/j.rinam.2022.100338_b7 – volume: 63 start-page: 171 issue: 1 year: 2020 ident: 10.1016/j.rinam.2022.100338_b23 article-title: A fourth-order numerical scheme for singularly perturbed delay parabolic problem arising in population dynamics publication-title: J Appl Math Comput doi: 10.1007/s12190-019-01313-7 – volume: 9 issue: 1 year: 2022 ident: 10.1016/j.rinam.2022.100338_b12 article-title: A novel numerical approach for singularly perturbed parabolic convection-diffusion problems on layer-adapted meshes publication-title: Res Math – year: 2021 ident: 10.1016/j.rinam.2022.100338_b25 article-title: A uniformly convergent collocation method for singularly perturbed delay parabolic reaction-diffusion problem – volume: 15 year: 2022 ident: 10.1016/j.rinam.2022.100338_b14 article-title: Parameter-uniform numerical scheme for singularly perturbed parabolic convection–diffusion Robin type problems with a boundary turning point publication-title: Results Appl Math doi: 10.1016/j.rinam.2022.100324 |
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| SubjectTerms | Exponentially fitted cubic spline method Parabolic convection–diffusion problem Singular perturbation Time delay Two small parameters |
| Title | A uniformly convergent numerical scheme for two parameters singularly perturbed parabolic convection–diffusion problems with a large temporal lag |
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