AM  Vol.2 No.7 , July 2011
Fourier Truncation Method for Fractional Numerical Differentiation
ABSTRACT
We consider a ill-posed problem-fractional numerical differentiation with a new method. We propose Fourier truncation method to compute fractional numerical derivatives. A Holder-type stability estimate is obtained. A numerical implementation is described. Numerical examples show that the proposed method is effective and stable.

Cite this paper
nullA. Qian and J. Mao, "Fourier Truncation Method for Fractional Numerical Differentiation," Applied Mathematics, Vol. 2 No. 7, 2011, pp. 914-917. doi: 10.4236/am.2011.27124.
References
[1]   J. Baumeister, “Stable Solution of Inverse Problems,” F. Vieweg and Sohn, Braunschweig, 1987.

[2]   R. Gorenflo and S. Vessela, “Abel Integral Equations,” Springer-Verlag, Berlin, Heidelberg, New York, 1991.

[3]   A. K. Louis, “Inverse und Schlecht Gesteellte Problem,” Teubner Verlag, Wiesbaden, 1989.

[4]   D. A. Murio, “Automatic Numerical Differentiation by Discrete Molification,” Computers and Mathematics with Applications, Vol. 13, No. 4, 1987, pp. 381-386. doi:10.1016/0898-1221(87)90006-X

[5]   D. A. Murio and L. Guo, “Discrete Stability Analysis of Molification Method for Numerical Differentiation,” Journal of Computational Applied Mathematics, Vol. 19, No. 6, 1990, pp. 15-25.

[6]   I. Daubechies, “Ten Lectures on Wavelets (CBMS-NSF Regional Conference Series in Applied Mathematics),” SIAM: Society for Industrial and Applied Mathematics, Philadelphia, 1992.

[7]   J. N. Lyness, “Has Numerical Differentiation a Future?” Utilitas Mathematics, Winnipeg, 1978.

[8]   J. Oliver, “An Algorithm for Numerical Differentiation of a Funcion of One Real Variable,” Journal of Computational Applied Mathematics, Vol. 6, No. 2, 1980, pp. 145-160. doi:10.1016/0771-050X(80)90008-X

[9]   T. Strom and J. N. Lyness, “On Numerical Differentiation,” BIT Numerical Mathematics, Vol. 15, No. 3, 1975, pp. 314-322. doi:10.1007/BF01933664

[10]   D. N. Hao, “A Molification Method for Ill-Posed Problems,” Numerische Mathematik, Vol. 68. No. 4, 1994, pp. 469-506. doi:10.1007/s002110050073

[11]   D. A. Murio, C. E. Mejia and S. Zhan, “Discrete Molification and Automatic Numerical Differentiation," Computers and Mathematics Application, Vol. 35, No. 5, 1998, pp. 1-16. doi:10.1016/S0898-1221(98)00001-7

[12]   L. Elden, F. Berntsson and T. Reginska, “Wavelet and Fourier Methods For Solving the Sideways Heat Equation,” SIAM Journal on Scientific Computing, Vol. 21, No. 6, 2000, pp. 2187-2205.

 
 
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