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Volumn 219, Issue 4, 2012, Pages 2087-2099

Numerical approach for solving diffusion problems using cubic B-spline collocation method

Author keywords

Biot number; Collocation; Cubic B spline; Diffusion equation; Peclet number

Indexed keywords

BIOT NUMBER; COLLOCATION; COMPUTATIONAL SCHEMES; COMPUTATIONAL TIME; CONTROL POINT; CUBIC B -SPLINE; CUBIC B-SPLINE COLLOCATIONS; DIFFUSION EQUATIONS; DIFFUSION MODEL; DIFFUSION PROBLEMS; KNOT VECTORS; NUMERICAL APPROACHES; NUMERICAL SCHEME; PORE DIFFUSION; POROUS STRUCTURES;

EID: 84867573344     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.08.053     Document Type: Article
Times cited : (9)

References (34)
  • 1
    • 18244384205 scopus 로고    scopus 로고
    • Radial basis function Hermite collocation approach for the solution of time dependent convection-diffusion problems
    • A. La Rocca, A.H. Rosales, and H. Power Radial basis function Hermite collocation approach for the solution of time dependent convection-diffusion problems Engrg. Anal. Bound. Elem. 29 2005 359 370
    • (2005) Engrg. Anal. Bound. Elem. , vol.29 , pp. 359-370
    • La Rocca, A.1    Rosales, A.H.2    Power, H.3
  • 2
    • 77955519254 scopus 로고    scopus 로고
    • A two-stage Lie-group shooting method (TSLGSM) to identify time-dependent thermal diffusivity
    • Chein-Shan. Liu A two-stage Lie-group shooting method (TSLGSM) to identify time-dependent thermal diffusivity Int. J. Heat Mass Transfer 53 2010 4876 4884
    • (2010) Int. J. Heat Mass Transfer , vol.53 , pp. 4876-4884
    • Liu, C.-Shan.1
  • 3
    • 84867578683 scopus 로고    scopus 로고
    • A numerical algorithm for solving advection-diffusion equation with constant and variable coefficients
    • S.G. Ahmed A numerical algorithm for solving advection-diffusion equation with constant and variable coefficients Open Numer. Methods J. 4 2012 1 7
    • (2012) Open Numer. Methods J. , vol.4 , pp. 1-7
    • Ahmed, S.G.1
  • 4
    • 80255123668 scopus 로고    scopus 로고
    • Polynomial based differential quadrature method for numerical solution of nonlinear Burgers' equation
    • A. Korkmaz, and I. Dag Polynomial based differential quadrature method for numerical solution of nonlinear Burgers' equation J. Franklin Inst. 348 10 2011 2863 2875
    • (2011) J. Franklin Inst. , vol.348 , Issue.10 , pp. 2863-2875
    • Korkmaz, A.1    Dag, I.2
  • 5
    • 84858334328 scopus 로고    scopus 로고
    • Quartic B-spline differential quadrature method
    • A. Korkmaz, A. Murat Aksoy, and I. Dag Quartic B-spline differential quadrature method Int. J. Nonlinear Sci. 11 4 2011 403 411
    • (2011) Int. J. Nonlinear Sci. , vol.11 , Issue.4 , pp. 403-411
    • Korkmaz, A.1    Murat Aksoy, A.2    Dag, I.3
  • 6
    • 78650698074 scopus 로고    scopus 로고
    • Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM)
    • G. Guraslan, and M. Sari Numerical solutions of linear and nonlinear diffusion equations by a differential quadrature method (DQM) Int. J. Numer. Methods Biomed. Eng. 27 2011 69 77
    • (2011) Int. J. Numer. Methods Biomed. Eng. , vol.27 , pp. 69-77
    • Guraslan, G.1    Sari, M.2
  • 7
    • 0026112845 scopus 로고
    • An improved finite difference method for fixed bed multicomponent adsorption
    • L.M. Sun, and F. Meunier An improved finite difference method for fixed bed multicomponent adsorption AIChE J. 37 2 1991 244 254
    • (1991) AIChE J. , vol.37 , Issue.2 , pp. 244-254
    • Sun, L.M.1    Meunier, F.2
  • 8
    • 77953133901 scopus 로고    scopus 로고
    • Numerical solution of the Burgers' equation by automatic differentiation
    • A. Asaithambi Numerical solution of the Burgers' equation by automatic differentiation Appl. Math. Comput. 216 2010 2700 2708
    • (2010) Appl. Math. Comput. , vol.216 , pp. 2700-2708
    • Asaithambi, A.1
  • 9
    • 4444378330 scopus 로고    scopus 로고
    • Finite element approach to Burgers' equation
    • A. Dogan, and A. Galerkin Finite element approach to Burgers' equation Appl. Math. Comput. 157 2004 331 346
    • (2004) Appl. Math. Comput. , vol.157 , pp. 331-346
    • Dogan, A.1    Galerkin, A.2
  • 10
    • 53449090789 scopus 로고    scopus 로고
    • A Chebyshev spectral collocation method for solving Burgers' type equations
    • A.H. Khater, R.S. Temsah, and M.M. Hassan A Chebyshev spectral collocation method for solving Burgers' type equations J. Comput. Appl. Math. 222 2008 333 350
    • (2008) J. Comput. Appl. Math. , vol.222 , pp. 333-350
    • Khater, A.H.1    Temsah, R.S.2    Hassan, M.M.3
  • 11
    • 80052213097 scopus 로고    scopus 로고
    • Shock wave simulations using Sinc differential quadrature method
    • A. Korkmaz Shock wave simulations using Sinc differential quadrature method Int. J. Comput. Aided Eng. Softw. 28 6 2011 654 674
    • (2011) Int. J. Comput. Aided Eng. Softw. , vol.28 , Issue.6 , pp. 654-674
    • Korkmaz, A.1
  • 12
    • 0028194327 scopus 로고
    • Steady-state multiplicity analysis of the heterogeneous axial dispersion fixed-bed reactor
    • G. Juncu, S. Bildea, and O. Floarea Steady-state multiplicity analysis of the heterogeneous axial dispersion fixed-bed reactor Chem. Eng. Sci. 49 1 1994 123 130
    • (1994) Chem. Eng. Sci. , vol.49 , Issue.1 , pp. 123-130
    • Juncu, G.1    Bildea, S.2    Floarea, O.3
  • 13
    • 0035880281 scopus 로고    scopus 로고
    • Highly accurate solution of the axial dispersion model expressed in S-system canonical form by Taylor series method
    • F. Shirashi Highly accurate solution of the axial dispersion model expressed in S-system canonical form by Taylor series method J. Chem. Eng. 83 2001 175 183
    • (2001) J. Chem. Eng. , vol.83 , pp. 175-183
    • Shirashi, F.1
  • 14
    • 0033167949 scopus 로고    scopus 로고
    • Computationally efficient solution techniques for adsorption problems involving steep gradients bidisperse particles
    • F. Liu, and S.K. Bhatia Computationally efficient solution techniques for adsorption problems involving steep gradients bidisperse particles Comput. Chem. Eng. 23 1999 933 943
    • (1999) Comput. Chem. Eng. , vol.23 , pp. 933-943
    • Liu, F.1    Bhatia, S.K.2
  • 15
    • 78650175080 scopus 로고    scopus 로고
    • A novel numerical scheme for solving Burgers' equation
    • Xu. Min, Ren-Hong Wang, Ji-Hong Zhang, and Qin Fang A novel numerical scheme for solving Burgers' equation Appl. Math. Comput. 217 2011 4473 4482
    • (2011) Appl. Math. Comput. , vol.217 , pp. 4473-4482
    • Min, Xu.1    Wang, R.-H.2    Zhang, J.-H.3    Fang, Q.4
  • 16
    • 0035927551 scopus 로고    scopus 로고
    • Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: Adsorption with steep gradients in bidisperse solids
    • F. Liu, and S.K. Bhatia Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids Chem. Eng. Sci. 56 2001 3727 3735
    • (2001) Chem. Eng. Sci. , vol.56 , pp. 3727-3735
    • Liu, F.1    Bhatia, S.K.2
  • 17
    • 0037089767 scopus 로고    scopus 로고
    • Asymptotic behavior of the Galerkin and the finite element collocation methods for a parabolic equation
    • S.E. Onah Asymptotic behavior of the Galerkin and the finite element collocation methods for a parabolic equation Appl. Math. Comput. 127 2002 207 213
    • (2002) Appl. Math. Comput. , vol.127 , pp. 207-213
    • Onah, S.E.1
  • 18
    • 33845782948 scopus 로고    scopus 로고
    • A computationally efficient technique for solving two point boundary value problems in porous media
    • S. Arora, S.S. Dhaliwal, and V.K. Kukreja A computationally efficient technique for solving two point boundary value problems in porous media Appl. Math. Comput. 183 2006 1170 1180
    • (2006) Appl. Math. Comput. , vol.183 , pp. 1170-1180
    • Arora, S.1    Dhaliwal, S.S.2    Kukreja, V.K.3
  • 19
    • 0347360394 scopus 로고    scopus 로고
    • On the use of reduced order models in bifurcation analysis of distributed parameter systems
    • Y. Liu, and W.E. Jacobsen On the use of reduced order models in bifurcation analysis of distributed parameter systems Comput. Chem. Eng. 28 1 2004 161 169
    • (2004) Comput. Chem. Eng. , vol.28 , Issue.1 , pp. 161-169
    • Liu, Y.1    Jacobsen, W.E.2
  • 20
    • 79955703532 scopus 로고    scopus 로고
    • Numerical solution of Burgers' equation with factorized diagonal Padé approximation
    • K. Altiparmak Numerical solution of Burgers' equation with factorized diagonal Padé approximation Int. J. Numer. Methods Heat Fluid Flow 21 3 2011 310 319
    • (2011) Int. J. Numer. Methods Heat Fluid Flow , vol.21 , Issue.3 , pp. 310-319
    • Altiparmak, K.1
  • 21
    • 74249110520 scopus 로고    scopus 로고
    • Application of the non-polynomial spline approach to the solution of the Burgers equation
    • M.A. Ramadan, T.S. El-Danaf, and F.E.I. Abd Alaal Application of the non-polynomial spline approach to the solution of the Burgers equation Open Appl. Math. J. 1 2007 15 20
    • (2007) Open Appl. Math. J. , vol.1 , pp. 15-20
    • Ramadan, M.A.1    El-Danaf, T.S.2    Abd Alaal, F.E.I.3
  • 23
    • 0035281751 scopus 로고    scopus 로고
    • Orthogonal spline collocation methods for partial differential equations
    • B. Bialecki, and G. Fairweather Orthogonal spline collocation methods for partial differential equations J. Comput. Appl. Math. 128 2001 55 82
    • (2001) J. Comput. Appl. Math. , vol.128 , pp. 55-82
    • Bialecki, B.1    Fairweather, G.2
  • 25
    • 0036566649 scopus 로고    scopus 로고
    • A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries
    • S.A. Nielsen, and J.S. Hesthaven A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries J. Ultrason. 40 2002 177 180
    • (2002) J. Ultrason. , vol.40 , pp. 177-180
    • Nielsen, S.A.1    Hesthaven, J.S.2
  • 26
    • 0037214483 scopus 로고    scopus 로고
    • Effect of the coordination number of the pore network on the transport and deposition of particles in porous media
    • S.C. Chen, E.K.C. Lee, and Y.I. Chang Effect of the coordination number of the pore network on the transport and deposition of particles in porous media Sep. Purif. Technol. 30 2003 11 26
    • (2003) Sep. Purif. Technol. , vol.30 , pp. 11-26
    • Chen, S.C.1    Lee, E.K.C.2    Chang, Y.I.3
  • 28
    • 50549180337 scopus 로고
    • The diffusion model of longitudinal mixing in beds of finite length. Numerical values
    • H. Brenner The diffusion model of longitudinal mixing in beds of finite length. Numerical values Chem. Eng. Sci. 17 1962 229 243
    • (1962) Chem. Eng. Sci. , vol.17 , pp. 229-243
    • Brenner, H.1
  • 29
    • 0028496986 scopus 로고
    • Modelling the flow and the deposition of fillers in packed beds of pulp fibers
    • M. Al-Jabari, A.R.P. Van Heiningen, and T.G.M. Van De Ven Modelling the flow and the deposition of fillers in packed beds of pulp fibers J. Pulp Pap. Sci. 20 9 1994 J249 J253
    • (1994) J. Pulp Pap. Sci. , vol.20 , Issue.9
    • Al-Jabari, M.1    Van Heiningen, A.R.P.2    Van De Ven, T.G.M.3
  • 30
    • 0002807533 scopus 로고
    • Longitudinal dispersion, intraparticle diffusion, and liquid-phase mass transfer during flow through multiparticle systems
    • G.L. Pellett Longitudinal dispersion, intraparticle diffusion, and liquid-phase mass transfer during flow through multiparticle systems J. Tappi 49 2 1966 75 82
    • (1966) J. Tappi , vol.49 , Issue.2 , pp. 75-82
    • Pellett, G.L.1
  • 31
    • 0029848003 scopus 로고    scopus 로고
    • Analytic solution to a model for the startup period of fixed bed reactors
    • Y. Zheng, and T. Gu Analytic solution to a model for the startup period of fixed bed reactors Chem. Eng. Sci. 51 15 1996 3773 3779
    • (1996) Chem. Eng. Sci. , vol.51 , Issue.15 , pp. 3773-3779
    • Zheng, Y.1    Gu, T.2
  • 32
    • 0020844128 scopus 로고
    • Numerical simulation of a fixed bed adsorption column by the method of orthogonal collocation
    • N.S. Raghvan, and D.M. Ruthven Numerical simulation of a fixed bed adsorption column by the method of orthogonal collocation AIChE J. 29 6 1983 922 925
    • (1983) AIChE J. , vol.29 , Issue.6 , pp. 922-925
    • Raghvan, N.S.1    Ruthven, D.M.2
  • 33
    • 0009125646 scopus 로고
    • Displacement washing of packed beds of cellulose fibers, Part-1: Mathematical model
    • L.E. Grahs Displacement washing of packed beds of cellulose fibers, Part-1: Mathematical model Sven. Papperstidn. 78 12 1975 446 450
    • (1975) Sven. Papperstidn. , vol.78 , Issue.12 , pp. 446-450
    • Grahs, L.E.1


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