Alternating direction implicit methods for two-dimensional diffusion with a non-local boundary condition

International Journal of Computer Mathematics

Volumn 72, Issue 3, 1999, Pages 349-366

  Dehghan, M ^a  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

2D diffusion equation; ADI schemes; Finite difference method; Non local boundary value problems; Numerical integration

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFUSION; FINITE DIFFERENCE METHOD; OPTICAL RESONATORS; PARTIAL DIFFERENTIAL EQUATIONS;

ADI SCHEME; ALTERNATING DIRECTION IMPLICIT (ADI) SCHEMES; ALTERNATING DIRECTION IMPLICIT METHOD; DIFFUSION EQUATIONS; FOURTH ORDER FINITE DIFFERENCE SCHEME; NON-LOCAL BOUNDARY CONDITIONS; NONLOCAL; NUMERICAL INTEGRATIONS;

NUMERICAL METHODS;

EID: 0003071909     PISSN: 00207160     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207169908804858     Document Type: Article

References (20)

1. Wang, S. and Lin, Y. (1989). A finite difference solution to an inverse problem determining a control function in a parabolic partial differential equation, Inverse Problems, 5, 631-640.
2. Cannon, J. R. and van der Hoek, J. (1986). Diffusion subject to the specification of mass, J. Math. Anal. Appl., 115, 517-529.
3. Cannon, J. R., Prez-Esteva, S. and van der Hoek, J. (1987). A Galerkin procedure for the diffusion equation subject to the specification of mass, Siam. J. Num. Anal., 24, 499-515.
4. Cannon, J. R. and van der Hoek, J. (1982). Implicit finite difference schemes for the diffusion of mass in porous media, Numerical Solutions of Partial Differential Equations (Edited by Noye, B. J.) North Holland, pp. 527-539.
5. Cannon, J. R. and Matheson, A. (1993). On the numerical solution of diffusion subject to the specification of mass, International Journal of Engineering Science, 31, 347-355.
6. Cannon, J. R., Lin, Y. and Wang, S. (1990). An implicit finite difference scheme for the diffusion equation subject to mass specification, International Journal of Engineering Science, 28, 573-578.
7. Day, W. A. (1983). A decreasing property of solutions of a parabolic equation with applications in thermoelasticity and other theories, Q. Appl. Math., 41, 475-486.
8. Peaceman, D. and Rachford, H. R. (1955). The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. App. Math., 3, 28-41.
9. Douglas, J. and Rachford, H. (1956). On the numerical solution of heat conduction problem in two and three space variables, Trans. Amer. Math. Soc., 82, 421-439.
10. Mitchell, A. R. and Fairweather, G. (1964). Improved forms of the alternating direction implicit methods of Douglas and Rachford for solving parabolic and elliptic equations, Numer. Maths., 6, 285-292.
11. Mitchell, A R. and Griffiths, D. F. (1980). The Finite Difference Methods in Partial Differential Equations, Wiley.
12. van Rosenberg, D. U. (1969). Methods for the numerical solution of partial differential equations, Modern Analytic and Computational Methods in Science and Mathematics, Ed. Bellman, R., American Elsevier Publishing Company, 16, New York.
13. Morris, J. L. and Gourlay, A. R. (1973). Modified locally one-dimemsional methods for parabolic partial differential equations in two-space variables, J. Inst. Maths. Applics., 12, 349-353.
14. Yanenko, N. N. (1971). The methods of fractional steps: The solutions of problems of mathematical physics in several variables, Springer-Verlag, New York.
15. Fairweather, G. and Mitchell, A. R. (1967). A new computational procedure for ADI methods, Siam. J. Num. Anal., 4(2), 163-170.
16. Warming, R. F. and Hyett, B. J. (1974). The modified equation approach to the stability and accuracy analysis of finite difference methods, Journal of Computational Physics, 14(2), 159-179.
17. Cannon, J. R., Lin, Y. and Matheson, A. (1993). The solution of the diffusion equation subject to specification of mass, Applicable Analysis, 50(2), 1-11.
18. Gerald, C. F. (1995). Applied Numerical Analysis, Addison-Wesley, California, 5th edition.
19. Wang, S. (1990). A numerical method for the heat conduction subject to moving boundary energy specification, Numerical Heat Transfer, 130, 35-38.
20. Noye, B. J. and Hayman, K. J. (1994). New lod and adi methods for the two dimensional diffusion equation, Int. J. Comp. Math., 51, 215-228.