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Regular Papers

Optimal modified method for a fractional-diffusion inverse heat conduction problem

Pages 521-533 | Received 30 Oct 2008, Accepted 03 Jan 2010, Published online: 19 Apr 2010

References

  • Murio, DA, 2007. Stable numerical solution of a fractional-diffusion inverse heat conduction problem, Comput. Math. Appl. 53 (2007), pp. 1492–1501.
  • Oldham, KB, and Spanier, J, 1970. The replacement of Fick's law by a formulation involving semidifferentiation, J. Electroanal. Chem. 26 (1970), pp. 331–341.
  • Oldham, KB, and Spanier, J, 1972. A general solution of the diffusion equation for semiinfinite geometries, J. Math. Anal. Appl. 39 (1972), pp. 655–669.
  • Liu, F, Anh, V, and Turner, I, 2004. Numerical solution of the space fractional Fokker-Planck equation, J. Comput. Appl. Math. 166 (2004), pp. 209–219.
  • Meerschaert, MM, and Tadjeran, C, 2004. Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math. 172 (2004), pp. 65–77.
  • Murio, DA, 2009. Stable numerical evaluation of Grünwald–Letnikov fractional derivatives applied to a fractional IHCP, Inverse Probl. Sci Eng. 17 (2009), pp. 229–243.
  • Tautenhahn, U, 1998. Optimality for ill-posed problems under general source conditions, Numer. Funct. Anal. Optim. 19 (1998), pp. 377–398.
  • Beck, JV, Blackwell, B, and Clair, SR, 1985. Inverse Heat Conduction: Ill-posed Problems. New York: Wiley; 1985.
  • Alifanov, OM, Artioukhine, EA, and Rumyantsev, SV, 1995. Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems. New York: Begel House; 1995.
  • Eldén, L, Berntsson, F, and Regińska, T, 2000. Wavelet and Fourier methods for solving the sideways heat equation, SIAM J. Sci. Comput. 21 (2000), pp. 2187–2205.
  • Qian, Z, and Fu, CL, 2007. Regularization strategies for a two-dimensional inverse heat conduction problem, Inverse Probl. 23 (2007), pp. 1053–1068.
  • Seidman, TI, and Eldén, L, 1990. An ‘optimal filtering’ method for the sideways heat equation, Inverse Probl. 6 (1990), pp. 681–696.
  • Tautenhahn, U, 1997. Optimal stable approximations for the sideways heat equation, J. Inverse Ill-posed Probl. 5 (1997), pp. 287–307.
  • Qian, Z, 2009. An optimal modified method for a two-dimensional inverse heat conduction problem, J. Math. Phys. 50 (2009), p. 023502, 1–9.

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