[1]
|
R. C. Mittal and R. K. Jain, “Redefined Cubic B-Splines Collocation Method for Solving Convection-Diffusion Equations,” Applied Mathematical Modelling, 2012, in Press. doi:10.1016/j.apm.2012.01.009
|
[2]
|
M. A. Celia, T. F. Russell, I. Herrera and R. E. Ewing, “An Eulerian-Langrangian Localized Adjoint Method for the Advection-Diffusion Equation,” Advances in Water Resources, Vol. 13, No. 4, 1990, pp. 187-206.
doi:10.1016/0309-1708(90)90041-2
|
[3]
|
M. Dehgan, “Weighted Finite Difference Techniques for the One-Dimensional Advection Diffusion Equation,” Applied Mathematics and Computation, Vol. 147, No. 2, 2004, pp. 307-319. doi:10.1016/S0096-3003(02)00667-7
|
[4]
|
M. K. Kadalbajoo and P. Arora, “Taylor-Galerkin BSpline Finite Element Method for the One-Dimensional Advection-Diffusion Equation,” Numerical Methods for Partial Differential Equations, Vol. 26, No. 5, 2010, pp. 1206-1223.
|
[5]
|
H. Nguyen and J. Reynen, “A Space Time Least-Squares Finite-Element Scheme for Advection-Diffusion Equation,” Computer Methods in Applied Mechanics and Engineering, Vol. 42, 1984, pp. 331-442.
doi:10.1016/0045-7825(84)90012-4
|
[6]
|
Rizwan-Uddin, “A Second-Order Space and Time Nodal Method for the One-Dimensional Convection-Diffusion Equation,” Computers & Fluids, Vol. 26, No. 3, 1997, pp. 233-247. doi:10.1016/S0045-7930(96)00039-4
|
[7]
|
R. Codina, “Comparison of Some Finite-Element Methods for Solving the Diffusion-Convection-Reaction Equation,” Computer Methods in Applied Mechanics and Engineering, Vol. 156, No. 1, 1998, pp. 185-210.
doi:10.1016/S0045-7825(97)00206-5
|
[8]
|
M. M. Chawla, M. A. Al-Zanaidi and D. J. Evans, “Generalized Trapezoidal Formulas for Convection-Diffusion Equations,” International Journal of Computer Mathematics, Vol. 72, No. 2, 1999, pp. 141-154.
doi:10.1080/00207169908804841
|
[9]
|
M. M. Chawla, M. A. Al-Zanaidi and M. G. Al-Aslab, “Extended One Step Time-Integration Schemes for Convection-Diffusion Equations,” Computers & Mathematics with Applications, Vol. 39, No. 3-4, 2000, pp. 71-84.
doi:10.1016/S0898-1221(99)00334-X
|
[10]
|
H. N. A. Ismail, E. M. E. Elbarbary and G. S. E. Salem, “Restrictive Taylor’s Approximation for Solving Convection-Diffusion Equation,” Applied Mathematics and Computation, Vol. 147, No. 2, 2004, pp. 355-363.
doi:10.1016/S0096-3003(02)00672-0
|
[11]
|
S. Karaa and J. Zhang, “High Order ADI Method for Solving Unsteady Convection-Diffusion Problems,” Journal of Computational Physics, Vol. 198, No. 1, 2004, pp. 1-9. doi:10.1016/j.jcp.2004.01.002
|
[12]
|
M. Dehghan, “Numerical Solution of the Three-Dimensional Advection-Diffusion Equation,” Applied Mathematics and Computation, Vol. 150, No. 1, 2004, pp. 5-19.
doi:10.1016/S0096-3003(03)00193-0
|
[13]
|
M. Dehghan, “On the Numerical Solution of the OneDimensional Convection-Diffusion Equation,” Mathematical Problems in Engineering, Vol. 2005, No. 1, 2005, pp. 61-74. doi:10.1155/MPE.2005.61
|
[14]
|
M. Dehghan, “Quasi-Implicit and Two-Level Explicit Finite-Difference Procedures for Solving the One-Dimensional Advection Equation,” Applied Mathematics and Computation, Vol. 167, No. 1, 2005, pp. 46-67.
doi:10.1016/j.amc.2004.06.067
|
[15]
|
D. K. Salkuyeh, “On the Finite Difference Approximation to the Convection-Diffusion Equation,” Applied Mathematics and Computation, Vol. 179, No. 1, 2006, pp. 7986. doi:10.1016/j.amc.2005.11.078
|
[16]
|
I. Dag, D. Irk and M. Tombul, “Least-Squares Finite-Element Method for the Advection-Diffusion Equation,” Applied Mathematics and Computation, Vol. 173, No. 1, 2006, pp. 554-565. doi:10.1016/j.amc.2005.04.054
|
[17]
|
H. Karahan, “Implicit Finite Difference Techniques for the Advection-Diffusion Equation Using Spreadsheets,” Advances in Engineering Software, Vol. 37, No. 9, 2006, pp. 601-608. doi:10.1016/j.advengsoft.2006.01.003
|
[18]
|
H. Karahan, “A Third-Order Upwind Scheme for the Advection-Diffusion Equation Using Spreadsheets,” Advances in Engineering Software, Vol. 38, No. 10, 2007, pp. 688-697. doi:10.1016/j.advengsoft.2006.10.006
|
[19]
|
H. Karahan, “Unconditional Stable Explicit Finite Difference Technique for the Advection-Diffusion Equation Using Spreadsheets,” Advances in Engineering Software, Vol. 38, No. 2, 2007, pp. 80-86.
doi:10.1016/j.advengsoft.2006.08.001
|
[20]
|
M. Dehghan and A. Mohebbi, “High-Order Compact Boundary Value Method for the Solution of Unsteady Convection-Diffusion Problems,” Mathematics and Computers in Simulation, Vol. 79, No. 3, 2008, pp. 683-699.
doi:10.1016/j.matcom.2008.04.015
|
[21]
|
M. Dehghan and F. Shakeri, “Application of He’s Variational Iteration Method for Solving the Cauchy ReactionDiffusion Problem,” Journal of Computational and Applied Mathematics, Vol. 214, No. 2, 2008, pp. 435-446.
doi:10.1016/j.cam.2007.03.006
|
[22]
|
H. F. Ding and Y. X. Zhang, “A New Difference Scheme with High Accuracy and Absolute Stability for Solving Convection-Diffusion Equations,” Journal of Computational and Applied Mathematics, Vol. 230, No. 2, 2009, pp. 600-606. doi:10.1016/j.cam.2008.12.015
|
[23]
|
A. Mohebbi and M. Dehghan, “High-Order Compact Solution of the One-Dimensional Heat and AdvectionDiffusion Equations,” Applied Mathematical Modelling, Vol. 34, No. 10, 2010, pp. 3071-3084.
doi:10.1016/j.apm.2010.01.013
|
[24]
|
M. Sari, G. Güraslan and A. Zeytinoglu, “High-Order Finite Difference Schemes for Solving the Advection-Diffusion Equation,” Computers & Mathematics with Applications, Vol. 15, No. 3, 2010, pp. 449-460.
|
[25]
|
S. Chandra Sekhara Rao and M. Kumar, “Exponential BSpline Collocation Method for Self-Adjoint Singularly Perturbed Boundary Value Problems,” Applied Numerical Mathematics, Vol. 58, No. 10, 2008, pp. 1572-1581.
doi:10.1016/j.apnum.2007.09.008
|
[26]
|
S. Chandra Sekhara Rao and M. Kumar, “Parameter-Uniformly Convergent Exponential Spline Difference Scheme for Singularly Perturbed Semilinear Reaction-Diffusion Problems,” Nonlinear Analysis, Vol. 71, 2009, pp. 15791588. doi:10.1016/j.na.2009.01.210
|
[27]
|
B. J. Mc Cartin, “Theory of Exponential Splines,” Journal of Approximation Theory, Vol. 66, No. 1, 1991, pp. 1-23. doi:10.1016/0021-9045(91)90050-K
|
[28]
|
S. Pruess, “Properties of Splines in Tension,” Journal of Approximation Theory, Vol. 17, No. 1, 1976, pp. 86-96.
doi:10.1016/0021-9045(76)90113-1
|
[29]
|
B. J. Mc Cartin, “Theory, Computation, and Application of Exponential Splines,” Courant Mathematics and Computing Laboratory Research and Development Report, DOE/ER/03077-171, 1981.
|