A wavelet operational method for solving fractional partial differential equations numerically

Applied Mathematics and Computation

Volumn 214, Issue 1, 2009, Pages 31-40

  Wu, J L ^a  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

Author keywords

Fractional partial differential equations; Haar wavelets; Lyapunov equation; Numerical method; Operational matrix

Indexed keywords

ALGEBRAIC EQUATIONS; ANALYTICAL SOLUTIONS; FRACTIONAL CALCULUS; FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS; FRACTIONAL PDE; HAAR WAVELETS; INTEGER ORDER; LYAPUNOV; LYAPUNOV EQUATION; MATRIX EQUATIONS; OPERATIONAL MATRICES; OPERATIONAL MATRIX; OPERATIONAL MATRIX OF INTEGRATION; OPERATIONAL METHODS; ORTHOGONAL FUNCTIONS; SCIENCE AND ENGINEERING; SIMULATION METHODS; UNIFIED FRAMEWORK;

COMPUTATIONAL FLUID DYNAMICS; COMPUTER PROGRAMMING; DIFFERENTIATION (CALCULUS); FOURIER ANALYSIS; IMAGE SEGMENTATION; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; NUMBER THEORY; NUMERICAL METHODS; SYSTEMS ENGINEERING;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 67349274987     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.03.066     Document Type: Article

References (20)

1. Podlubny I. Fractional Differential Equations (1999), Academic press
2. Meerschaert M.M., and Tadjeran C. Finite difference approximations for two-sided space-fractional partial differential equations. Applied Numerical Mathematics 56 (2006) 80-90
3. Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Computers and Mathematics with Applications 51 (2006) 1367-1376
4. Jumarie G. Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution. Journal of Applied Mathematics and Computing 24 (2007) 31-48
5. Baeumera B., Kov'acsa M., and Meerschaertb M.M. Numerical solutions for fractional reaction-diffusion equations. Computers and Mathematics with Applications 55 (2008) 2212-2226
6. I.B. Petris, M. Vinagre, L. Dorcak, V. Fwliu, Fractional digital control of a heat solid: Experimental results, in: The Proceedings of International Carpathian Control Conference, Malenovice, Czech Republic, 2002, pp. 365-370.
7. Chen C.F., and Hsiao C.H. Design of piecewise constant gains for optimal control via Walsh functions. IEEE Transactions on Automatic Control AC-20 (1975) 596-603
8. Chen C.F., Tsay Y.T., and Wu T.T. Walsh operational matrices for fractional calculus and their application to distributed parameter systems. Journal of Franklin Institute 503 (1977) 267-284
9. Shih D.S., Kung F.C., and Chao C.M. Laguerre series approach to the analysis of a linear control system incorporation observers. International Journal of Control 43 (1986) 123-128
10. Ckang R.Y., and Wang M.L. Legendre polynomials approximation to dynamic linear state equations with initial or boundary value condition. International Journal of Control 40 (1984) 215-232
11. Paraskevopoulos P.N. Chebyshev series approach to system identification analysis and optimal control. Journal of Franklin Institute 316 (1983) 135-157
12. Mouroutsos S.G., and Sparis P.D. Taylor series approach to system identification analysis and optimal control. Journal of Franklin Institute 319 (1985) 359-371
13. Paraskevopoulos P.N., Sparis P.D., and Mouroutsos S.G. The Fourier series operational matrix of integration. International Journal of System Science 16 (1985) 171-176
14. Chen C.F., and Hsiao C.H. Haar wavelet method for solving lumped and distributed parameter systems. IEE Proceedings - Control Theory and Applications 144 (1997) 87-94
15. Wu J.L., Chen C.H., and Chen C.F. Numerical inversion of Laplace transform using Haar wavelet operational matrices. IEEE Transactions on Circuits and Systems-Part I: Fundamental Theory and Applications 48 (2001) 120-122
16. Akansu A.N., and Haddad R.A. Multiresolution Signal Decomposition: Transform, Subbands and Wavelets (1981), Academic Press Inc. pp. 60-61
17. Vetterli M., and Kovacevic J. Wavelets and Subband Coding (1995), Prentice-Hall, Englewood Cliffs, New Jersey pp. 32-34
18. Bartels R.H., and Stewart G.W. Solution of the matrix equation AX + XB = C. Communications of the ACM 15 (1972) 669-713
19. Teukolsky S.A., Vettering W.T., and Flannery B.P. Numerical Recipes in C, The Art of Scientific Computing. Second ed. (1992), W.H. Press
20. Jumarie G. Fourier's transform of fractional order via Mittag-Leffler function and modified Riemann-Liouville derivative. Journal of Applied Mathematics and Informatics 26 (2008) 1101-1121