Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms

Applied Numerical Mathematics

Volumn 57, Issue 1, 2007, Pages 19-35

  in 't Hout, K J ^a   Welfert, B D ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

ADI splitting schemes; Convection diffusion equations; Fourier transformation; Initial boundary value problems; Numerical solution; Von Neumann stability analysis

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; FOURIER TRANSFORMS; INITIAL VALUE PROBLEMS; PROBLEM SOLVING;

ALTERNATING DIRECTION IMPLICIT (ADI) SCHEMES; CONVECTION-DIFFUSION EQUATIONS; INITIAL-BOUNDARY VALUE PROBLEMS; NUMERICAL SOLUTION; VON NEUMANN STABILITY ANALYSIS;

BOUNDARY VALUE PROBLEMS;

EID: 33750505893     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2005.11.011     Document Type: Article

References (19)

1. Brian P.L.T. A finite-difference method of high-order accuracy for the solution of three-dimensional transient heat conduction problems. AIChE J. 7 (1961) 367-370
2. Craig I.J.D., and Sneyd A.D. An alternating-direction implicit scheme for parabolic equations with mixed derivatives. Comput. Math. Appl. 16 (1988) 341-350
3. Douglas J. Alternating direction methods for three space variables. Numer. Math. 4 (1962) 41-63
4. Douglas J., and Rachford H.H. On the numerical solution of heat conduction problems in two and three space variables. Trans. Amer. Math. Soc. 82 (1956) 421-439
5. Elf J., Lötstedt P., and Sjöberg P. Problems of high dimension in molecular biology. In: Hackbusch W. (Ed). Proceedings of the 19th GAMM-Seminar, Max-Planck-Institute for Mathematic in the Sciences, Leipzig (2003) 21-30. http://www.mis.mpg.de/conferences/gamma/2003/
6. in 't Hout K.J. On the contractivity of implicit-explicit linear multistep methods. Appl. Numer. Math. 42 (2002) 201-212
7. K.J. in 't Hout, B.D. Welfert, Unconditional stability of ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms, in preparation
8. van der Houwen P.J., and Verwer J.G. One-step splitting methods for semi-discrete parabolic equations. Computing 22 (1979) 291-309
9. Hundsdorfer W. Stability of approximate factorization with θ-methods. BIT 39 (1999) 473-483
10. Hundsdorfer W. Accuracy and stability of splitting with Stabilizing Corrections. Appl. Numer. Math. 42 (2002) 213-233
11. Hundsdorfer W., and Verwer J.G. Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer Ser. Comput. Math. vol. 33 (2003), Springer, Berlin
12. Jorge J.C., and Lisbona F. Contractivity results for alternating direction schemes in Hilbert spaces. Appl. Numer. Math. 15 (1994) 65-75
13. Lanser D., Blom J.G., and Verwer J.G. Time integration of the shallow water equations in spherical geometry. J. Comput. Phys. 171 (2001) 373-393
14. McKee S., and Mitchell A.R. Alternating direction methods for parabolic equations in two space dimensions with a mixed derivative. Comput. J. 13 (1970) 81-86
15. McKee S., Wall D.P., and Wilson S.K. An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms. J. Comput. Phys. 126 (1996) 64-76
16. Mitchell A.R., and Griffiths D.F. The Finite Difference Method in Partial Differential Equations (1980), Wiley, New York
17. Peaceman D.W. Fundamentals of Numerical Reservoir Simulation. Developments in Petroleum Science vol. 6 (1977), Elsevier, Amsterdam
18. C. Randall, PDE Techniques for Pricing Derivatives with Exotic Path Dependencies or Exotic Processes, Lecture Notes, Workshop CANdiensten, Amsterdam, May 2002
19. Tavella D., and Randall C. Pricing Financial Instruments: The Finite Difference Method (2000), Wiley, New York