Numerical procedures for the determination of an unknown coefficient in parabolic differential equations

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Application and Algorithm

Volumn 9, Issue 4, 2002, Pages 555-573

  Azari, Hossein ^a  

^a INSTITUTE FOR STUDIES IN THEORETICAL PHYSICS AND MATHEMATICS IPM   (Iran)

Author keywords

Convergence; Inverse problem; Maximum principle; Numerical method

Indexed keywords

EID: 0347936090     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. J. R. Cannon and Yanping Lin, Determination of a parameter p(t) in some quasilinear parabolic differential equations, Inverse Problems 4 (1988), no. 1, 35-45. MR 89h:35333
2. _, Determination of parameter p(t) in Hōlder classes for some semilinear parabolic equations, Inverse Problems 4 (1988), no. 3, 595-606. MR 90a:35222
3. J. R. Cannon, Yanping Lin, and Shingmin Wang, Determination of source parameter in parabolic equation, Meccanica 27 (1992), 85-94.
4. John R. Cannon, Salvador Pérez Esteva, and John van der Hoek, A Galerkin procedure for the diffusion equation subject to the specification of mass, SIAM J. Numer. Anal. 24 (1987), no. 3, 499-515. MR 88e:65132
5. S. H. Crandall, An optimum implicit recurrence formulae for heat conduction equation, Q. Appl. Math. 13 (1955), 318-320.
6. K. L. Deckert and C. G. Maple, Solution for diffusion with integral type boundary conditions, Proc. IOwa Acad. Sci. 70 (1963), 354-361.
7. M. Dehghan, An inverse problem of finding a source parameter in a semilinear parabolic equation, Applied Mathematical Modelling 25 (2001), no. 9, 743-754.
8. A. Friedman, Partial differential equations of parabolic type, Prentice Hall, Englewood Cliffs. NJ, 1964.
9. N. I. Ionkin, Solution of a boundary-value problem in heat conduction with a non-classical boundary condition, J. Differential Equations 13 (1977), 204-211.
10. O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Uralecva, Linear and quasilinear equations of parabolic type, AMS, Providence RI, 1986.
11. L. Lapidus and G. F. Pinder, Numerical solution of partial differential equations in science and engineering, Wiley, New York, 1982.
12. Yanping Lin, Analytical and numerical solutions for a class of nonlocal nonlinear parabolic differential equations, SIAM J. Math. Anal. 25 (1994), no. 6, 1577-1594. MR 95i:35167
13. Yanping Lin and James H. Liu, Stability of nonlocal diffusion equations, Dynam. Contin. Discrete Impuls. Systems 5 (1999), no. 1-4, 53-66, Differential equations and dynamical systems (Waterloo, ON, 1997). MR 2000c:35104
14. Yanping Lin, Shuzhan Xu, and Hong-Ming Yin, Finite difference approximations for a class of non-local parabolic equations, Internat. J. Math. Math. Sci. 20 (1997), no. 1, 147-163. MR 97i:65135
15. A. R. Mitchell and D. F. Griffiths, The finite difference methods in partial differential equations, Wiley, New York, 1980.
16. A. Shidfar and H. Azari, An inverse problem for a nonlinear diffusion equation, Nonlinear Analysis theo., meth., and appl. 28 (1997), no. 4, 589-593.
17. Shingmin Wang and Yanping Lin, A finite-difference solution to an inverse problem for determining a control function in a parabolic partial differential equation, Inverse Problems 5 (1989), no. 4, 631-640. MR 90d:35299
18. B. J. Hyett R. F. Warming, The modified equation approach to the stability and accuracy analysis of finite difference methods, J. Comput. Phys. 14 (1974), no. 2, 159-179.