Wavelet method for a class of fractional convection-diffusion equation with variable coefficients

Journal of Computational Science

Volumn 1, Issue 3, 2010, Pages 146-149

  Chen, Yiming ^a   Wu, Yongbing ^a   Cui, Yuhuan ^b   Wang, Zhuangzhuang ^a   Jin, Dongmei ^a  

^a YANSHAN UNIVERSITY   (China)

^b HEBEI POLYTECHNIC UNIVERSITY   (China)

Author keywords

Convection diffusion equation; Fractional derivative; Haar wavelet; Numerical solution; Operational matrix; Variable coefficients

Indexed keywords

CONVECTION-DIFFUSION EQUATIONS; FRACTIONAL DERIVATIVES; HAAR WAVELETS; NUMERICAL SOLUTION; OPERATIONAL MATRICES; VARIABLE COEFFICIENTS;

DIFFUSION IN LIQUIDS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS;

HEAT CONVECTION;

EID: 77956405259     PISSN: 18777503     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jocs.2010.07.001     Document Type: Article

References (19)

1. Li B., Luo J. Wavelet Analysis and its Application 2005, Electronic Industrial Publication, Beijing.
2. Ge Z., Sha W. Wavelet Analysis Theory and MATLAB Application 2007, Electronic Industrial Publication, Beijing.
3. Chen J. Analysis of stability and convergence of numerical approximation for the Riesz fractional reaction-dispersion equation. Journal of Xiamen University (Natural Science) 2007, 46(5):616-619.
4. Xing Y., Wu X., Xu Z. Multiclass least squares auto-correlation wavelet support vector machines. ICIC Express Letters 2008, 2(4):345-350.
5. Zhuang P., Liu F. An explicit approximation for the space-time fractional diffusion equation. Numerical Mathematics A: Journal of Chinese Universities 2005, 27:223-228.
6. Zhong W., Lin W. Nonlocal and multiple-point boundary value problem for fractional differential equations. Computers and Mathematics with Applications 2010, 59(3):1345-1351.
7. N'Géreékata G.M. A Cauchy problem for some fractional abstract differential equations with fractional order with nonlocal conditions. Nonlinear Analysis 2009, 70(5):1873-1876.
8. Benchohra M., Hamani S., Ntouyas S.K. Boundary value problems for differential equations with fractional order and nonlocal conditions. Nonlinear Analysis TMA 2009, 71(7):2391-2396.
9. Vasundhara Devi J., Lakshmikantham V. Nonsmooth analysis and fractional differential equations. Nonlinear Analysis 2009, 70(12):4151-4157.
10. Mustapha O., Lefebvre D., Khalil M., Hoblos G., Chafouk H. Fault detection algorithm using DCS method combined with filters bank derived from the wavelet transform. International Journal of Innovative Computing, Information and Control 2009, 5(5):1313-1328.
11. Dong J., Wei X., Zhang Q., Zhao Y. Pitch detection using circular average magnitude difference function based on wavelet transform. International Journal of Innovative Computing, Information and Control 2009, 5(9):2717-2724.
12. Zhou Y., Jiao F., Li J. Existence and uniqueness for p-type fractional neutral differential equations. Nonlinear Analysis 2009, 71(8):2724-2733.
13. Zhou Y., Jiao F., Li J. Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Analysis 2009, 71(7-8):3249-3256.
14. Podlubny I. Fractional Differential Equations 1999, Academic Press, San Diego.
15. Chen C.F., Hsiao C.H. Design of piecewise constant gains for optimal control via Walsh functions. IEEE Transactions on Automatic Control 1975, AC-20:596-603.
16. Kilicman A., Al Zhour Z.A.A. Kronecker operational matrices for fractional calculus and some applications. Applied Mathematics and Computation 2007, 187(1):250-265.
17. Wu J.L., Hsiao C.H. Haar wavelet method for solving lumped and distributed parameter systems. IEE Proceedings-Control Theory and Applications 1997, 144:87-94.
18. Odibat Z., Momani S. A generalized differential transform method for linear partial differential equations of fractional order. Applied Mathematics Letters 2008, 21(2):194-199.
19. Qin P., Zhang X. A numerical method for the space-time fractional convection-diffusion equation. Mathematic Numerica Sinica 2008, 30(3):305-310. (in Chinese).