Fourth-order compact schemes for solving multidimensional heat problems with neumann boundary conditions

Numerical Methods for Partial Differential Equations

Volumn 24, Issue 1, 2008, Pages 165-178

  Zhao, Jennifer ^a   Dai, Weizhong ^b   Zhang, Suyang ^b  

^a UNIVERSITY OF MICHIGAN DEARBORN   (United States)

^b Louisiana Tech University   (United States)

Author keywords

Compact finite difference schemes; Heat conducting problems of two or three dimensions; Local one dimensional method; Neumann boundary conditions

Indexed keywords

EID: 38049120167     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20255     Document Type: Article

References (15)

1. 1 J. Zhao, W. Dai, and T. Niu, Fourth order compact schemes of a heat conduction problem with Neumann bundary conditions, Numer Methods Partial Differential Equations, to appear.
2. 2 L. Lapidus and G. F. Pinder, Numerical solution of partial differential equations in science and engineering, Wiley, New York, 1982.
3. 3 J. C. Strikwerda, Finite difference schemes and partial differential equations, Chapman & Hall, New York, 1989.
4. 4 M. H. Carpenter, D. Gottlieb, and S. Abarbanel, Stable and accurate boundary treatments for compact, high‐order finite difference schemes, Appl Numer Math 12 ( 1993), 55–87.
5. 5 I. Christie, Upwind compact finite difference schemes, J Comput Phys 53 ( 1985), 353–368.
6. 6 P. C. Chu and C. Fan, A three‐point combined compact difference scheme, J Comput Phys 140 ( 1998), 370–399.
7. 7 G. F. Carey and W. F. Spotz, High‐order compact mixed methods, Commun Numer Methods Eng 13 ( 1997), 553–564.
8. 8 P. C. Chu and C. Fan, A three‐point six‐order nonuniform combined compact difference scheme, J Comput Phys 148 ( 1999), 663–674.
9. 9 W. Dai and R. Nassar, A compact finite difference scheme for solving a three‐dimensional heat transport equation in a thin film, Numer Methods Partial Differential Equations 16 ( 2000), 441–458.
10. 10 W. Dai and R. Nassar, Compact ADI method for sloving parabolic differential equations, Numer Methods Partial Differential Equations 18 ( 2002), 129–142.
11. 11 X. Deng and H. Maekawa, Compact high‐order accurate nonlinear scheme, J Comput Phys 130 ( 1997), 77–91.
12. 12 D. Gaitonde and J. S. Shang, Optimized compact‐difference‐based finite volume schemes for linear wave phenomena, J Comput Phys 138 ( 1997), 617–643.
13. 13 L. Ge and J. Zhang, High accuracy iterative solution of convection diffusion equation with boundary layer on nonuniform grids, J Comput Phys 171 ( 2001), 560–578.
14. 14 H. Sun, J. Zhang, and J. Zhao, High order compact scheme with multigrid local mesh refinement procedure for convection diffusion problems, Computer Methods Appl Mech Eng 191 ( 2002), 4661–4674.
15. 15 K. E. Atkinson, An introduction to numerical analysis, 2nd Ed, Wiley, New York, 1988.