Numerical solutions of singularly perturbed one-dimensional parabolic convection–diffusion problems by the Bessel collocation method
In this paper, we present a numerical scheme for the approximate solutions of the one-dimensional parabolic convection–diffusion model problems. This method is based on the Bessel collocation method used for some problems of ordinary differential equations. In fact, the approximate solution of the p...
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| Published in | Applied mathematics and computation Vol. 220; pp. 305 - 315 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.09.2013
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| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2013.06.027 |
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| Abstract | In this paper, we present a numerical scheme for the approximate solutions of the one-dimensional parabolic convection–diffusion model problems. This method is based on the Bessel collocation method used for some problems of ordinary differential equations. In fact, the approximate solution of the problem in the truncated Bessel series form is obtained by this method. By substituting truncated Bessel series solution into the problem and by using the matrix operations and the collocation points, the suggested scheme reduces the problem to a linear algebraic equation system. By solving this equation system, the unknown Bessel coefficients can be computed. An error estimation technique is given for the considered problem and the method. To show the accuracy and the efficiency of the method, numerical examples are implemented and the comparisons are given by the other methods. |
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| AbstractList | In this paper, we present a numerical scheme for the approximate solutions of the one-dimensional parabolic convection–diffusion model problems. This method is based on the Bessel collocation method used for some problems of ordinary differential equations. In fact, the approximate solution of the problem in the truncated Bessel series form is obtained by this method. By substituting truncated Bessel series solution into the problem and by using the matrix operations and the collocation points, the suggested scheme reduces the problem to a linear algebraic equation system. By solving this equation system, the unknown Bessel coefficients can be computed. An error estimation technique is given for the considered problem and the method. To show the accuracy and the efficiency of the method, numerical examples are implemented and the comparisons are given by the other methods. |
| Author | Yüzbaşı, Şuayip Şahin, Niyazi |
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| Cites_doi | 10.1086/260062 10.1016/j.camwa.2011.07.016 10.1016/S0377-0427(02)00861-0 10.1016/j.mcm.2011.08.007 10.1016/j.cam.2007.08.016 10.1016/j.camwa.2011.03.097 10.1016/j.camwa.2011.05.057 10.1007/BF01395986 10.1002/mma.1519 10.1016/j.apm.2011.03.030 10.1002/nme.1620240408 10.1016/j.jmaa.2009.01.038 10.1016/S0377-0427(01)00502-7 10.1002/nme.1620241105 |
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| References | Yüzbaşı, Şahin, Sezer (b0085) 2011; 3 Yüzbaşı (b0100) 2011; 34 Yüzbaşı (b0105) 2011; 62 Shahmorad (b0115) 2005; 167 Baumert, Braun, Glos, Müller, Stoyan (b0130) 1981; vol. 23 Kadalbajoo, Gupta (b0050) 2009; 355 Yüzbaşı, Şahin, Sezer (b0095) 2011; 61 El-Gamel (b0060) 2006; 181 Jacob (b0015) 1959 Hirsch (b0010) 1988; vol. 1 Hahn, Bigeon, Sabonnadiere (b0025) 1987; 24 Launder, Spalding (b0035) 1972 Clavero, Jorge, Lisbona (b0040) 2003; 154 Çelik (b0125) 2006; 174 Kadalbajoo, Gupta, Awasthi (b0045) 2008; 220 Phongthanapanich, Dechaumphai (b0065) 2009; 209 Polak, Den Heiger, Schilders, Markowich (b0020) 1987; 24 Ramos (b0075) 2005; 161 Yüzbaşı, Şahin, Sezer (b0090) 2012; 55 Oliveira (b0120) 1980; 36 Lenferink (b0055) 2002; 143 Şahin, Yüzbaşı, Gülsu (b0110) 2011; 62 Du, Wu, Chen (b0080) 2011; 35 Black, Scholes (b0030) 1973; 81 Kadalbajoo, Awasthi (b0070) 2006; 183 Clavero (10.1016/j.amc.2013.06.027_b0040) 2003; 154 Yüzbaşı (10.1016/j.amc.2013.06.027_b0100) 2011; 34 Kadalbajoo (10.1016/j.amc.2013.06.027_b0070) 2006; 183 Baumert (10.1016/j.amc.2013.06.027_b0130) 1981; vol. 23 Yüzbaşı (10.1016/j.amc.2013.06.027_b0095) 2011; 61 Kadalbajoo (10.1016/j.amc.2013.06.027_b0050) 2009; 355 Lenferink (10.1016/j.amc.2013.06.027_b0055) 2002; 143 Çelik (10.1016/j.amc.2013.06.027_b0125) 2006; 174 Launder (10.1016/j.amc.2013.06.027_b0035) 1972 Hahn (10.1016/j.amc.2013.06.027_b0025) 1987; 24 Ramos (10.1016/j.amc.2013.06.027_b0075) 2005; 161 Jacob (10.1016/j.amc.2013.06.027_b0015) 1959 Phongthanapanich (10.1016/j.amc.2013.06.027_b0065) 2009; 209 Şahin (10.1016/j.amc.2013.06.027_b0110) 2011; 62 Shahmorad (10.1016/j.amc.2013.06.027_b0115) 2005; 167 Black (10.1016/j.amc.2013.06.027_b0030) 1973; 81 Oliveira (10.1016/j.amc.2013.06.027_b0120) 1980; 36 El-Gamel (10.1016/j.amc.2013.06.027_b0060) 2006; 181 Hirsch (10.1016/j.amc.2013.06.027_b0010) 1988; vol. 1 Polak (10.1016/j.amc.2013.06.027_b0020) 1987; 24 Yüzbaşı (10.1016/j.amc.2013.06.027_b0090) 2012; 55 Kadalbajoo (10.1016/j.amc.2013.06.027_b0045) 2008; 220 Yüzbaşı (10.1016/j.amc.2013.06.027_b0105) 2011; 62 Du (10.1016/j.amc.2013.06.027_b0080) 2011; 35 Yüzbaşı (10.1016/j.amc.2013.06.027_b0085) 2011; 3 |
| References_xml | – volume: 220 start-page: 271 year: 2008 end-page: 289 ident: b0045 article-title: A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection–diffusion problem publication-title: J. Comput. Appl. Math. – year: 1959 ident: b0015 article-title: Heat Transfer – volume: 35 start-page: 4589 year: 2011 end-page: 4602 ident: b0080 article-title: A novel mathematical modeling of multiple scales for a class of two dimensional singular perturbed problems publication-title: Appl. Math. Modell. – volume: vol. 1 year: 1988 ident: b0010 publication-title: Numerical Computation of Internal and External Flows – volume: 62 start-page: 755 year: 2011 end-page: 769 ident: b0110 article-title: A collocation approach for solving systems of linear Volterra integral equations with variable coefficients publication-title: Comput. Math. Appl. – volume: 183 start-page: 42 year: 2006 end-page: 60 ident: b0070 article-title: A parameter uniform difference scheme for singularly perturbed parabolic problem in one space dimension publication-title: Appl. Math. Comput. – volume: 62 start-page: 2289 year: 2011 end-page: 2303 ident: b0105 article-title: A numerical approach for solving the high-order linear singular differential–difference equations publication-title: Comput. Math. Appl. – volume: 143 start-page: 49 year: 2002 end-page: 68 ident: b0055 article-title: A second order scheme for a time-dependent, singularly perturbed convection–diffusion equation publication-title: J. Comput. Appl. Math. – volume: vol. 23 year: 1981 ident: b0130 article-title: Modelling and Computation of Water Quality Problems in River Networks publication-title: Lecture Notes in Control and Inform. Sci. – volume: 55 start-page: 330 year: 2012 end-page: 341 ident: b0090 article-title: A collocation approach for solving modelling the pollution of a system of lakes publication-title: Math. Comput. Modell. – volume: 24 start-page: 763 year: 1987 end-page: 838 ident: b0020 article-title: Semiconductor device modelling from the numerical point of view publication-title: Int. J. Numer. Methods Eng. – volume: 161 start-page: 501 year: 2005 end-page: 512 ident: b0075 article-title: A piecewise-analytical method for singularly perturbed parabolic problems publication-title: Appl. Math. Comput. – volume: 3 start-page: 81 year: 2011 end-page: 101 ident: b0085 article-title: A Bessel polynomial approach for solving linear neutral delay differential equations with variable coefficients publication-title: J. Adv. Res. Diff. Equ. – volume: 24 start-page: 2071 year: 1987 end-page: 2086 ident: b0025 article-title: An ‘upwind’ finite element method for electromagnetic field problems in moving media publication-title: Int. J. Numer. Methods Eng. – volume: 154 start-page: 415 year: 2003 end-page: 429 ident: b0040 article-title: A uniformly convergent scheme on a nonuniform mesh for convection–diffusion parabolic problems publication-title: J. Comput. Appl. Math. – volume: 355 start-page: 439 year: 2009 end-page: 452 ident: b0050 article-title: Numerical solution of singularly perturbed convection–diffusion problem using parameter uniform B-spline collocation method publication-title: J. Math. Anal. Appl. – year: 1972 ident: b0035 article-title: Mathematical Models of Turbulence – volume: 181 start-page: 1635 year: 2006 end-page: 1644 ident: b0060 article-title: A Wavelet-Galerkin method for a singularly perturbed convection-dominated diffusion equation publication-title: Appl. Math. Comput. – volume: 61 start-page: 3079 year: 2011 end-page: 3096 ident: b0095 article-title: Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases publication-title: Comput. Math. Appl. – volume: 36 start-page: 27 year: 1980 end-page: 31 ident: b0120 article-title: Collacation and residual correction publication-title: Numer. Math. – volume: 81 start-page: 637 year: 1973 end-page: 659 ident: b0030 article-title: The price of options and corporate liabilities publication-title: J. Polit. Econ. – volume: 34 start-page: 2218 year: 2011 end-page: 2230 ident: b0100 article-title: A numerical approach for solving a class of the nonlinear Lane–Emden type equations arising in astrophysics publication-title: Math. Meth. Appl. Sci. – volume: 167 start-page: 1418 year: 2005 end-page: 1429 ident: b0115 article-title: Numerical solution of general form linear Fredholm. Volterra integro differantial equations by the tau method with an error estimation publication-title: Appl. Math. Comput. – volume: 174 start-page: 910 year: 2006 end-page: 920 ident: b0125 article-title: Collacation method and residual correction using Chebyshev series publication-title: Appl. Math. Comput. – volume: 209 start-page: 177 year: 2009 end-page: 185 ident: b0065 article-title: Combined finite volume element method for singularly perturbed reaction–diffusion problems publication-title: Appl. Math. Comput. – volume: 81 start-page: 637 year: 1973 ident: 10.1016/j.amc.2013.06.027_b0030 article-title: The price of options and corporate liabilities publication-title: J. Polit. Econ. doi: 10.1086/260062 – volume: 62 start-page: 2289 issue: 5 year: 2011 ident: 10.1016/j.amc.2013.06.027_b0105 article-title: A numerical approach for solving the high-order linear singular differential–difference equations publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2011.07.016 – volume: 154 start-page: 415 year: 2003 ident: 10.1016/j.amc.2013.06.027_b0040 article-title: A uniformly convergent scheme on a nonuniform mesh for convection–diffusion parabolic problems publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(02)00861-0 – volume: 55 start-page: 330 issue: 3–4 year: 2012 ident: 10.1016/j.amc.2013.06.027_b0090 article-title: A collocation approach for solving modelling the pollution of a system of lakes publication-title: Math. Comput. Modell. doi: 10.1016/j.mcm.2011.08.007 – volume: vol. 23 year: 1981 ident: 10.1016/j.amc.2013.06.027_b0130 article-title: Modelling and Computation of Water Quality Problems in River Networks – year: 1972 ident: 10.1016/j.amc.2013.06.027_b0035 – volume: 167 start-page: 1418 year: 2005 ident: 10.1016/j.amc.2013.06.027_b0115 article-title: Numerical solution of general form linear Fredholm. Volterra integro differantial equations by the tau method with an error estimation publication-title: Appl. Math. Comput. – volume: 220 start-page: 271 year: 2008 ident: 10.1016/j.amc.2013.06.027_b0045 article-title: A uniformly convergent B-spline collocation method on a nonuniform mesh for singularly perturbed one-dimensional time-dependent linear convection–diffusion problem publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2007.08.016 – volume: 61 start-page: 3079 issue: 10 year: 2011 ident: 10.1016/j.amc.2013.06.027_b0095 article-title: Numerical solutions of systems of linear Fredholm integro-differential equations with Bessel polynomial bases publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2011.03.097 – volume: 62 start-page: 755 issue: 2 year: 2011 ident: 10.1016/j.amc.2013.06.027_b0110 article-title: A collocation approach for solving systems of linear Volterra integral equations with variable coefficients publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2011.05.057 – volume: 36 start-page: 27 year: 1980 ident: 10.1016/j.amc.2013.06.027_b0120 article-title: Collacation and residual correction publication-title: Numer. Math. doi: 10.1007/BF01395986 – volume: vol. 1 year: 1988 ident: 10.1016/j.amc.2013.06.027_b0010 – volume: 34 start-page: 2218 issue: 18 year: 2011 ident: 10.1016/j.amc.2013.06.027_b0100 article-title: A numerical approach for solving a class of the nonlinear Lane–Emden type equations arising in astrophysics publication-title: Math. Meth. Appl. Sci. doi: 10.1002/mma.1519 – volume: 35 start-page: 4589 year: 2011 ident: 10.1016/j.amc.2013.06.027_b0080 article-title: A novel mathematical modeling of multiple scales for a class of two dimensional singular perturbed problems publication-title: Appl. Math. Modell. doi: 10.1016/j.apm.2011.03.030 – volume: 209 start-page: 177 year: 2009 ident: 10.1016/j.amc.2013.06.027_b0065 article-title: Combined finite volume element method for singularly perturbed reaction–diffusion problems publication-title: Appl. Math. Comput. – volume: 3 start-page: 81 issue: 1 year: 2011 ident: 10.1016/j.amc.2013.06.027_b0085 article-title: A Bessel polynomial approach for solving linear neutral delay differential equations with variable coefficients publication-title: J. Adv. Res. Diff. Equ. – volume: 24 start-page: 763 year: 1987 ident: 10.1016/j.amc.2013.06.027_b0020 article-title: Semiconductor device modelling from the numerical point of view publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620240408 – volume: 355 start-page: 439 year: 2009 ident: 10.1016/j.amc.2013.06.027_b0050 article-title: Numerical solution of singularly perturbed convection–diffusion problem using parameter uniform B-spline collocation method publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2009.01.038 – volume: 161 start-page: 501 year: 2005 ident: 10.1016/j.amc.2013.06.027_b0075 article-title: A piecewise-analytical method for singularly perturbed parabolic problems publication-title: Appl. Math. Comput. – volume: 174 start-page: 910 year: 2006 ident: 10.1016/j.amc.2013.06.027_b0125 article-title: Collacation method and residual correction using Chebyshev series publication-title: Appl. Math. Comput. – volume: 181 start-page: 1635 year: 2006 ident: 10.1016/j.amc.2013.06.027_b0060 article-title: A Wavelet-Galerkin method for a singularly perturbed convection-dominated diffusion equation publication-title: Appl. Math. Comput. – volume: 143 start-page: 49 year: 2002 ident: 10.1016/j.amc.2013.06.027_b0055 article-title: A second order scheme for a time-dependent, singularly perturbed convection–diffusion equation publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(01)00502-7 – year: 1959 ident: 10.1016/j.amc.2013.06.027_b0015 – volume: 24 start-page: 2071 year: 1987 ident: 10.1016/j.amc.2013.06.027_b0025 article-title: An ‘upwind’ finite element method for electromagnetic field problems in moving media publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620241105 – volume: 183 start-page: 42 year: 2006 ident: 10.1016/j.amc.2013.06.027_b0070 article-title: A parameter uniform difference scheme for singularly perturbed parabolic problem in one space dimension publication-title: Appl. Math. Comput. |
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| Title | Numerical solutions of singularly perturbed one-dimensional parabolic convection–diffusion problems by the Bessel collocation method |
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