메뉴 건너뛰기




Volumn 62, Issue 3, 2011, Pages 1075-1083

Tau approximate solution of fractional partial differential equations

Author keywords

Fractional partial differential equations; Improved algebraic formulation; Operational approach of the Tau method; Spectral methods

Indexed keywords

APPROXIMATE SOLUTION; CHEBYSHEV; FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS; IMPROVED ALGEBRAIC FORMULATION; LEGENDRE POLYNOMIALS; MATRIX; MATRIX VECTOR MULTIPLICATION; NONLINEAR TERMS; NUMERICAL RESULTS; NUMERICAL SOLUTION; SPECTRAL METHODS; TAU METHOD;

EID: 79960988872     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.03.013     Document Type: Article
Times cited : (55)

References (30)
  • 4
    • 33947164737 scopus 로고    scopus 로고
    • Fractional-order dynamical models of love
    • DOI 10.1016/j.chaos.2006.01.098, PII S0960077906001652
    • W.M. Ahmad, and R. El-Khazali Fractional-order dynamical models of love Chaos Solitons Fractals 33 2007 1367 1375 (Pubitemid 46413017)
    • (2007) Chaos, Solitons and Fractals , vol.33 , Issue.4 , pp. 1367-1375
    • Ahmad, W.M.1    El-Khazali, R.2
  • 5
    • 32644481603 scopus 로고    scopus 로고
    • The time-fractional diffusion equation and fractional advectiondispersion equation
    • F. Huang, and F. Liu The time-fractional diffusion equation and fractional advectiondispersion equation ANZIAM J. 46 2005 1 14
    • (2005) ANZIAM J. , vol.46 , pp. 1-14
    • Huang, F.1    Liu, F.2
  • 6
    • 77749270676 scopus 로고    scopus 로고
    • The fractional transport equation: An analytical solution and spectral approximation by Chebyshev polynomials
    • A. Kadem The fractional transport equation: an analytical solution and spectral approximation by Chebyshev polynomials Appl. Sci. 11 2009 78 90
    • (2009) Appl. Sci. , vol.11 , pp. 78-90
    • Kadem, A.1
  • 7
    • 70349986628 scopus 로고    scopus 로고
    • Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation
    • A. Kadem, and D. Baleanu Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation Commun. Nonlinear Sci. Numer. Simul. 15 3 2010 491 501
    • (2010) Commun. Nonlinear Sci. Numer. Simul. , vol.15 , Issue.3 , pp. 491-501
    • Kadem, A.1    Baleanu, D.2
  • 8
    • 51749116733 scopus 로고    scopus 로고
    • Finite difference approximations for the fractional FokkerPlanck equation
    • S. Chen, F. Liu, P. Zhuang, and V. Anh Finite difference approximations for the fractional FokkerPlanck equation Appl. Math. Modelling 33 2009 256 273
    • (2009) Appl. Math. Modelling , vol.33 , pp. 256-273
    • Chen, S.1    Liu, F.2    Zhuang, P.3    Anh, V.4
  • 9
    • 24144494623 scopus 로고    scopus 로고
    • An explicit and numerical solutions of the fractional KdV equation
    • DOI 10.1016/j.matcom.2005.05.001, PII S0378475405001643
    • S. Momani An explicit and numerical solutions of the fractional KdV equation Math. Comput. Simulation 70 2005 110 118 (Pubitemid 41230033)
    • (2005) Mathematics and Computers in Simulation , vol.70 , Issue.2 , pp. 110-118
    • Momani, S.1
  • 10
    • 35349007529 scopus 로고    scopus 로고
    • Generalized differential transform method for solving a space and time-fractional diffusionwave equation
    • S. Momani, Z. Odibat, and V.S. Erturk Generalized differential transform method for solving a space and time-fractional diffusionwave equation Phys. Lett. A 370 2007 379 387
    • (2007) Phys. Lett. A , vol.370 , pp. 379-387
    • Momani, S.1    Odibat, Z.2    Erturk, V.S.3
  • 11
    • 56049100715 scopus 로고    scopus 로고
    • Homotopy analysis method for solving linear and nonlinear fractional diffusionwave equation
    • H. Jafari, and S. Seifi Homotopy analysis method for solving linear and nonlinear fractional diffusionwave equation Commun. Nonlinear Sci. Numer. Simul. 14 2009 2006 2012
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 2006-2012
    • Jafari, H.1    Seifi, S.2
  • 12
    • 34748865972 scopus 로고    scopus 로고
    • Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
    • DOI 10.1016/j.camwa.2006.12.037, PII S0898122107002520, Variational Iteration Method for Nonlinear Problems
    • S. Momani, and Zaid Odibat Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations Comput. Math. Appl. 54 2007 910 919 (Pubitemid 47488806)
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.7-8 , pp. 910-919
    • Momani, S.1    Odibat, Z.2
  • 13
    • 56049100715 scopus 로고    scopus 로고
    • Homotopy analysis method for solving linear and nonlinear fractional diffusionwave equation
    • H. Jafari, and S. Seifi Homotopy analysis method for solving linear and nonlinear fractional diffusionwave equation Commun. Nonlinear Sci. Numer. Simul. 14 2009 2006 2012
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 2006-2012
    • Jafari, H.1    Seifi, S.2
  • 14
    • 33748901201 scopus 로고    scopus 로고
    • The Adomian decomposition method for solving partial differential equations of fractal order in finite domains
    • DOI 10.1016/j.physleta.2006.06.024, PII S037596010600911X
    • A.M.A. El-Sayed, and M. Gaber The Adomian decomposition method for solving partial differential equations of fractal order in finite domains Phys. Lett. A 359 2006 175 182 (Pubitemid 44428061)
    • (2006) Physics Letters, Section A: General, Atomic and Solid State Physics , vol.359 , Issue.3 , pp. 175-182
    • El-Sayed, A.M.A.1    Gaber, M.2
  • 15
    • 33744981446 scopus 로고    scopus 로고
    • Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method
    • DOI 10.1016/j.amc.2005.11.025, PII S0096300305009276
    • S. Momani, and Z. Odibat Analytical solution of a time-fractional NavierStokes equation by Adomian decomposition method Appl. Math. Comput. 177 2 2006 488 494 (Pubitemid 43866876)
    • (2006) Applied Mathematics and Computation , vol.177 , Issue.2 , pp. 488-494
    • Momani, S.1    Odibat, Z.2
  • 16
    • 47849126401 scopus 로고    scopus 로고
    • A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
    • S. Momani, and Z. Odibat A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula J. Comput. Appl. Math. 220 2008 85 95
    • (2008) J. Comput. Appl. Math. , vol.220 , pp. 85-95
    • Momani, S.1    Odibat, Z.2
  • 17
    • 0019659830 scopus 로고
    • Operational approach to the Tau method for the numerical solution of nonlinear differential equations
    • E.L. Ortiz, and H. Samara An operational approach to the Tau method for the numerical solution of nonlinear differential equations Computing 27 1981 15 25 (Pubitemid 12519953)
    • (1981) Computing (Vienna/New York) , vol.27 , Issue.1 , pp. 15-25
    • Ortiz, E.L.1    Samara, H.2
  • 18
    • 85162699057 scopus 로고
    • Trigonometric interpolation of empirical and analytical functions
    • C. Lanczos Trigonometric interpolation of empirical and analytical functions J. Math. Phys. 17 1938 123 199
    • (1938) J. Math. Phys. , vol.17 , pp. 123-199
    • Lanczos, C.1
  • 19
    • 0003006282 scopus 로고
    • Approximation of eigenvalues defined by ordinary differential equations with the Tau method
    • B. Ka gestrm, A. Ruhe, Springer Berlin
    • K.M. Liu, and E.L. Ortiz Approximation of eigenvalues defined by ordinary differential equations with the Tau method B. Ka gestrm, A. Ruhe, Matrix Pencils 1983 Springer Berlin 90 102
    • (1983) Matrix Pencils , pp. 90-102
    • Liu, K.M.1    Ortiz, E.L.2
  • 20
    • 79952182967 scopus 로고    scopus 로고
    • Note on the solution of transport equation by Tau method and Walsh functions
    • 10.1155/2010/704168 Article ID 704168, 13 pages
    • A. Kadem, and A. Kiliman Note on the solution of transport equation by Tau method and Walsh functions Abstr. Appl. Anal. 2010 2010 10.1155/2010/704168 Article ID 704168, 13 pages
    • (2010) Abstr. Appl. Anal. , vol.2010
    • Kadem, A.1    Kiliman, A.2
  • 21
    • 38249034254 scopus 로고
    • Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlinearly
    • K.M. Liu, and E.L. Ortiz Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlinearly J. Comput. Phys. 72 1987 299 310
    • (1987) J. Comput. Phys. , vol.72 , pp. 299-310
    • Liu, K.M.1    Ortiz, E.L.2
  • 22
    • 0024775023 scopus 로고
    • Numerical solution of ordinary and partial functional-differential eigenvalue problems with the Tau method
    • K.M. Liu, and E.L. Ortiz Numerical solution of ordinary and partial functional-differential eigenvalue problems with the Tau method Computing 41 1989 205 217
    • (1989) Computing , vol.41 , pp. 205-217
    • Liu, K.M.1    Ortiz, E.L.2
  • 23
    • 0020905495 scopus 로고
    • Numerical solution of differential eigenvalue problems with an operational approach to the Tau method
    • E.L. Ortiz, and H. Samara Numerical solution of differential eigenvalue problems with an operational approach to the Tau method Computing 31 1983 95 103 (Pubitemid 14472687)
    • (1983) Computing (Vienna/New York) , vol.31 , Issue.2 , pp. 95-103
    • Ortiz, E.L.1    Samara, H.2
  • 24
    • 0022784186 scopus 로고
    • Numerical solution of eigenvalue problems for partial differential equations with the Tau-lines method
    • K.M. Liu, and E.L. Ortiz Numerical solution of eigenvalue problems for partial differential equations with the Tau-lines method Comput. Math. Appl. B 12 5/6 1986 1153 1168 (Pubitemid 17574127)
    • (1986) Computers & mathematics with applications , vol.12 B , Issue.5-6 , pp. 1153-1168
    • Liu, K.M.1    Ortiz, E.L.2
  • 25
    • 4244163123 scopus 로고
    • Numerical solution of nonlinear partial differential equations with Tau method
    • E.L. Ortiz, and K.S. Pun Numerical solution of nonlinear partial differential equations with Tau method J. Comput. Appl. Math. 12/13 1985 511 516
    • (1985) J. Comput. Appl. Math. , vol.1213 , pp. 511-516
    • Ortiz, E.L.1    Pun, K.S.2
  • 26
    • 0022782188 scopus 로고
    • Bi-dimensional Tau-elements method for the numerical solution of nonlinear partial differential equations with an application to Burger's equation
    • E.L. Ortiz, and K.S. Pun A bi-dimensional Tau-elements method for the numerical solution of nonlinear partial differential equations with an application to Burger's equation Comput. Math. Appl. B 12 5/6 1986 1225 1240 (Pubitemid 17574120)
    • (1986) Computers & mathematics with applications , vol.12 B , Issue.5-6 , pp. 1225-1240
    • Ortiz, E.L.1    Pun, K.-S.2
  • 27
    • 0021177673 scopus 로고
    • Numerical solution of partial differential equations with variable coefficients with an operational approach to the Tau method
    • E.L. Ortiz, and H. Samara Numerical solution of partial differential equations with variable coefficients with an operational approach to the Tau method Comput. Math. Appl. 10 1 1984 5 13 (Pubitemid 14526353)
    • (1984) Computers & mathematics with applications , vol.10 , Issue.1 , pp. 5-13
    • Ortiz, E.L.1    Samara, H.2
  • 28
    • 0031537729 scopus 로고    scopus 로고
    • Iterated solutions of linear operator equations with the Tau Method
    • M.K. EL-Daou, and H.G. Khajah Iterated solutions of linear operator equations with the Tau method Math. Comput. 66 217 1997 207 213 (Pubitemid 127423913)
    • (1997) Mathematics of Computation , vol.66 , Issue.217 , pp. 207-213
    • El-Daou, M.K.1    Khajah, H.G.2
  • 29
    • 0037443341 scopus 로고    scopus 로고
    • Numerical solution of a class of Integro-Differential equations by the Tau Method with an error estimation
    • DOI 10.1016/S0096-3003(02)00081-4, PII S0096300302000814
    • S.M. Hosseini, and S. Shahmorad Numerical solution of a class of integro-differential equations by the Tau method with an error estimation Appl. Math. Comput. 136 2003 559 570 (Pubitemid 35276466)
    • (2003) Applied Mathematics and Computation , vol.136 , Issue.2-3 , pp. 559-570
    • Hosseini, S.M.1    Shahmorad, S.2
  • 30
    • 33646878106 scopus 로고    scopus 로고
    • Analytical approach to linear fractional partial differential equations arising in fluid mechanics
    • DOI 10.1016/j.physleta.2006.02.048, PII S0375960106003148
    • S. Momani, and Z. Odibat Analytical approach to linear fractional partial differential equations arising in fluid mechanics Phys. Lett. A 355 2006 271 279 (Pubitemid 43783194)
    • (2006) Physics Letters, Section A: General, Atomic and Solid State Physics , vol.355 , Issue.4-5 , pp. 271-279
    • Momani, S.1    Odibat, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.