Stable numerical solution of a fractional-diffusion inverse heat conduction problem

Computers and Mathematics with Applications

Volumn 53, Issue 10, 2007, Pages 1492-1501

  Murio, Diego A ^a  

^a UNIVERSITY OF CINCINNATI   (United States)

Author keywords

Ill posed problems; Inverse heat conduction problem; Mollification; Numerical fractional differentiation

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DATA ACQUISITION; DIFFUSION; ERROR ANALYSIS; HEAT FLUX; PROBLEM SOLVING;

BOUNDARY TEMPERATURE; DIFFUSION EQUATION; DISCRETE PROBLEM; SEMI-INFINITE CONDUCTOR;

HEAT CONDUCTION;

EID: 34249102276     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.05.027     Document Type: Article

References (9)

1. Oldham K.B., and Spanier J. A general solution of the diffusion equation for semiinfinite geometries. J. Math. Anal. Appl. 39 (1972) 655-669
2. Oldham K.B., and Spanier J. The replacement of Fick's law by a formulation involving semidifferentiation. J. Electroanalytical Chem. 26 (1970) 331-341
3. Kulish V.V., and Lage J.L. Fractional-diffusion solution for transient local temperature and heat flux. Trans. ASME 122 (2000) 372-376
4. Liu F., Anh V., and Turner I. Numerical solution of the space fractional Fokker-Planck equation. J. Comput. Appl. Math. 166 (2004) 209-219
5. Meerschaert M.M., and Tadjeran C. Finite difference approximations for fractional advection-dispersion flow equations. J. Comput. Appl. Math. 172 (2004) 65-77
6. Podlubny I. Fractional Differential Equations (1999), Academic Press
7. Murio D.A. On the stable estimation of Caputo fractional derivatives. Comput. Math. Appl. 51 (2006) 539-1550
8. Murio D.A. The Mollification Method and the Numerical Solution of Ill-Posed Problems (1993), John Wiley and Sons, New York
9. Murio D.A. Mollification and Space Marching. In: Woodbury K. (Ed). Inverse Engineering Handbook (2002), CRC Press, Boca Raton, Florida 219-326 (Chapter 4)