A modified Crank-Nicolson scheme with incremental unknowns for convection dominated diffusion equations

Applied Mathematics and Computation

Volumn 215, Issue 9, 2010, Pages 3293-3301

  Song, Lun Ji ^a,b   Wu, Yu Jiang ^a  

^a LANZHOU UNIVERSITY   (China)

^b INDIANA UNIVERSITY   (United States)

Author keywords

Convection dominated diffusion equation; Crank Nicolson scheme; Error estimate; Incremental unknowns; One sided difference approximation; Stability

Indexed keywords

CONVECTION-DOMINATED DIFFUSION; CRANK-NICOLSON SCHEME; DIFFERENCE APPROXIMATION; ERROR ESTIMATES; INCREMENTAL UNKNOWNS;

CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; PARTIAL DIFFERENTIAL EQUATIONS;

DIFFERENCE EQUATIONS;

EID: 71649111630     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.10.017     Document Type: Article

References (16)

1. Bredehoeft J.D. Comment on: numerical solution to the convective diffusion equation. Water Resour. Res. 7 (1971) 755-756
2. Fezoui L., and Stoufflet B. A class of implicit upwind schemes for Euler simulations with unconstructed meshes. J. Comput. Phys. 84 (1989) 174-206
3. Hegarty A.F., Oriordan E., and Stynes M. A comparison of uniformly convergent difference schemes for two-dimensional convection-diffusion problems. J. Comput. Phys. 105 (1993) 24-32
4. Chen M., and Temam R. Incremental unknowns for solving partial differential equations. Numer. Math. 59 3 (1991) 255-271
5. Chen M., and Temam R. Incremental unknowns in finite differences: condition number of the matrix. SIAM J. Matrix Anal. A 14 2 (1993) 432-455
6. Song L.J., and Wu Y.J. Incremental unknowns method for solving three-dimensional convection-diffusion equations. Numer. Math. J. Chinese Univ. (Eng. Ser.) 16 1 (2007) 14-27
7. Song L.J., and Wu Y.J. Incremental unknowns in three-dimensional stationary problem. Numer. Algorithms 46 (2007) 153-171
8. Song L.J., and Wu Y.J. Incremental unknowns method based on the θ-scheme for time-dependent convection-diffusion equations. Math. Comput. Simulat. 79 7 (2009) 2001-2012
9. Fornberg B. Generation of finite difference formulas on arbitrarily spaced grids. Math. Comput. 51 (1988) 699-706
10. Rahul K., and Bhattacharyya S.N. One-sided finite-difference approximations suitable for use with Richardson extrapolation. J. Comput. Phys. 219 (2006) 13-20
11. Georgea K., and Twizell E.H. Stable second-order finite-difference methods for linear initial-boundary-value problems. Appl. Math. Lett. 19 (2006) 146-154
12. Saad Y., and Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Comput. 7 (1986) 856-869
13. Grigoriev M.M., and Dargush G.F. Efficiency of boundary element methods for time-dependent convective heat diffusion at high Peclet numbers. Commun. Numer. Meth. Eng. 21 (2005) 149-161
14. Axelsson O., and Nikolova M. Adaptive refinement for convection-diffusion problems based on a defect-correction technique and finite difference method. Computing 58 (1997) 1-30
15. Bieniasz L.K. High order accurate, one-sided finite-difference approximations to concentration gradients at the boundaries, for the simulation of electrochemical reaction-diffusion problems in one-dimensional space geometry. Comput. Biol. Chem. 27 3 (2003) 315-325
16. Osher S. Nonlinear singular perturbation problems and one sided difference schemes. SIAM J. Numer. Anal. 18 1 (1981) 129-144