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Volumn 12, Issue 2, 2012, Pages 168-173

Numerical solution of Fractional Ordinary Differential Equations using a Multiquadric approximation scheme

Author keywords

Fractional ordinary differential equations; Meshless methods; Multiquadric approximation scheme

Indexed keywords


EID: 84855874477     PISSN: 18125654     EISSN: 18125662     Source Type: Journal    
DOI: 10.3923/jas.2012.168.173     Document Type: Article
Times cited : (1)

References (34)
  • 1
    • 41949112904 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to fractional IVPs
    • Abdulaziz, O., I. Hashim and S. Momani, 2008. Application of homotopy perturbation method to fractional IVPs. J. Comput. Applied Math., 216: 574-584.
    • (2008) J. Comput. Applied Math. , vol.216 , pp. 574-584
    • Abdulaziz, O.1    Hashim, I.2    Momani, S.3
  • 2
    • 33947164737 scopus 로고    scopus 로고
    • Fractional-order dynamical models of love
    • Ahmad, W.M. and R. El-Khazali, 2007. Fractional-order dynamical models of love. Chaos Solitons Fractals, 33: 1367-1375.
    • (2007) Chaos Solitons Fractals , vol.33 , pp. 1367-1375
    • Ahmad, W.M.1    El-Khazali, R.2
  • 3
    • 55549097908 scopus 로고    scopus 로고
    • Numerical solution of elliptic partial differential equarions using direct and indirect radial basis function networks
    • Aminataei, A. and M.M. Mazarei, 2005. Numerical solution of elliptic partial differential equarions using direct and indirect radial basis function networks. Eur. J. Sci. Res., 2: 5-5.
    • (2005) Eur. J. Sci. Res. , vol.2 , pp. 5
    • Aminataei, A.1    Mazarei, M.M.2
  • 4
    • 54849427033 scopus 로고    scopus 로고
    • Numerical solution of Poisson's equation using radial basis function networks on the polar coordinate
    • Aminataei, A. and M.M. Mazarei, 2008. Numerical solution of Poisson's equation using radial basis function networks on the polar coordinate. Comput. Math. Appl., 11: 2887-2895.
    • (2008) Comput. Math. Appl. , vol.11 , pp. 2887-2895
    • Aminataei, A.1    Mazarei, M.M.2
  • 5
    • 34250215244 scopus 로고    scopus 로고
    • Solution of fractional differential equations by using differential transform method
    • Arikoglu, A. and I. Ozkol, 2007. Solution of fractional differential equations by using differential transform method. Chaos Solitons Fractals, 34: 1473-1481.
    • (2007) Chaos Solitons Fractals , vol.34 , pp. 1473-1481
    • Arikoglu, A.1    Ozkol, I.2
  • 7
    • 33748901201 scopus 로고    scopus 로고
    • The Adomian decomposition method for solving partial differential equations of fractal order in finite domains
    • El-Sayed, A.M.A. and M. Gaber, 2006. The Adomian decomposition method for solving partial differential equations of fractal order in finite domains. Phys. Lett. A, 359: 175-182.
    • (2006) Phys. Lett. A , vol.359 , pp. 175-182
    • El-Sayed, A.M.A.1    Gaber, M.2
  • 8
    • 84968515237 scopus 로고
    • Scattered data interpolation: Tests of some methods
    • Franke, R., 1982. Scattered data interpolation: Tests of some methods. Math. Comput., 38: 181-200.
    • (1982) Math. Comput. , vol.38 , pp. 181-200
    • Franke, R.1
  • 9
    • 52749093169 scopus 로고    scopus 로고
    • Toward a new analytical method for solving nonlinear fractional differential equations
    • Ghorbani, A., 2008. Toward a new analytical method for solving nonlinear fractional differential equations. Comput. Methods Applied Mech. Eng., 197: 4173-4179.
    • (2008) Comput. Methods Applied Mech. Eng. , vol.197 , pp. 4173-4179
    • Ghorbani, A.1
  • 10
    • 0001018295 scopus 로고
    • Multiquadric equations of topography and other irregular surfaces
    • Hardy, R.L., 1971. Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res., 76: 1905-1915.
    • (1971) J. Geophys. Res. , vol.76 , pp. 1905-1915
    • Hardy, R.L.1
  • 11
    • 0025206382 scopus 로고
    • Theory and applications of the multiquadric bi-harmonic method: 20 years of discovery
    • Hardy, R.L., 1990. Theory and applications of the multiquadric bi-harmonic method: 20 years of discovery. Comput. Math. Appl., 19: 163-208.
    • (1990) Comput. Math. Appl. , vol.19 , pp. 163-208
    • Hardy, R.L.1
  • 12
    • 56049100715 scopus 로고    scopus 로고
    • Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation
    • Jafari, H. and S. Seifi, 2009. Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation. Commun. Nonlinear Sci. Numer. Simul., 14: 2006-2012.
    • (2009) Commun. Nonlinear Sci. Numer. Simul. , vol.14 , pp. 2006-2012
    • Jafari, H.1    Seifi, S.2
  • 13
    • 0025229330 scopus 로고
    • Multiquadrics: A scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates
    • Kansa, E.J., 1990. Multiquadrics: A scattered data approximation scheme with applications to computational fluid-dynamics-I surface approximations and partial derivative estimates. Comput. Math. Appl., 19: 127-145.
    • (1990) Comput. Math. Appl. , vol.19 , pp. 127-145
    • Kansa, E.J.1
  • 14
    • 0025210711 scopus 로고
    • Multiquadrics: A scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to hyperbolic, parabolic and elliptic partial differential equations
    • Kansa, E.J., 1990. Multiquadrics: A scattered data approximation scheme with applications to computational fluid-dynamics-II solutions to hyperbolic, parabolic and elliptic partial differential equations. Comput. Math. Appl., 19: 147-161.
    • (1990) Comput. Math. Appl. , vol.19 , pp. 147-161
    • Kansa, E.J.1
  • 15
    • 84966244353 scopus 로고
    • Multivariable interpolation and conditionally positive definite functions
    • Madych, W.R. and S.A. Nelson, 1990. Multivariable interpolation and conditionally positive definite functions. II. Math. Comput, 54: 211-230.
    • (1990) II. Math. Comput , vol.54 , pp. 211-230
    • Madych, W.R.1    Nelson, S.A.2
  • 16
    • 0000172493 scopus 로고
    • Miscellaneous error bounds for multiquadric and related interpolators
    • Madych, W.R., 1992. Miscellaneous error bounds for multiquadric and related interpolators. Comput. Math. Appl., 24: 121-138.
    • (1992) Comput. Math. Appl. , vol.24 , pp. 121-138
    • Madych, W.R.1
  • 17
    • 0035137045 scopus 로고    scopus 로고
    • Numerical solution of differential equations using multiquadric radial basis function networks
    • Mai-Duy, N. and T. Tran-Cong, 2001. Numerical solution of differential equations using multiquadric radial basis function networks. Neutral Networks, 14: 185-199.
    • (2001) Neutral Networks , vol.14 , pp. 185-199
    • Mai-Duy, N.1    Tran-Cong, T.2
  • 18
    • 34250122797 scopus 로고
    • Interpolation of scatter data: Distance matrices and conditionally positive definite functions
    • Micchelli, C.A., 1986. Interpolation of scatter data: Distance matrices and conditionally positive definite functions. Constr. Approx., 2: 11-22.
    • (1986) Constr. Approx. , vol.2 , pp. 11-22
    • Micchelli, C.A.1
  • 20
    • 33744981446 scopus 로고    scopus 로고
    • Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method
    • Momani, S. and Z. Odibat, 2006. Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method. Applied Math. Comput., 177: 488-494.
    • (2006) Applied Math. Comput. , vol.177 , pp. 488-494
    • Momani, S.1    Odibat, Z.2
  • 21
    • 34748865972 scopus 로고    scopus 로고
    • Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations
    • Momani, S. and Z. Odibat, 2007. Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations. Comput. Math. Appl., 54: 910-919.
    • (2007) Comput. Math. Appl. , vol.54 , pp. 910-919
    • Momani, S.1    Odibat, Z.2
  • 22
    • 33748425302 scopus 로고    scopus 로고
    • Numerical comparison of methods for solving linear differential equations of fractional order
    • Momani, S. and Z. Odibat, 2007. Numerical comparison of methods for solving linear differential equations of fractional order. Chaos Solitons Fractals, 31: 1248-1255.
    • (2007) Chaos Solitons Fractals , vol.31 , pp. 1248-1255
    • Momani, S.1    Odibat, Z.2
  • 23
    • 47849126401 scopus 로고    scopus 로고
    • A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
    • Momani, S. and Z. Odibat, 2008. A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula. J. Comput. Applied Math., 220: 85-95.
    • (2008) J. Comput. Applied Math. , vol.220 , pp. 85-95
    • Momani, S.1    Odibat, Z.2
  • 24
    • 24144494623 scopus 로고    scopus 로고
    • An explicit and numerical solutions of the fractional KdV equation
    • Momani, S., 2005. An explicit and numerical solutions of the fractional KdV equation. Math. Comput. Simul., 70: 110-118.
    • (2005) Math. Comput. Simul. , vol.70 , pp. 110-118
    • Momani, S.1
  • 25
    • 35349007529 scopus 로고    scopus 로고
    • Generalized differential transform method for solving a space-and time-fractional diffusion-wave equation
    • Momani, S., Z. Odibat and V.S. Erturk, 2007. Generalized differential transform method for solving a space-and time-fractional diffusion-wave equation. Phys. Lett. A, 370: 379-387.
    • (2007) Phys. Lett. A , vol.370 , pp. 379-387
    • Momani, S.1    Odibat, Z.2    Erturk, V.S.3
  • 29
    • 0021424253 scopus 로고
    • Linear approximation of transfer function with a pole of fractional power
    • Sun, H.H., A.A. Abdelwahab and B. Onaral, 1984. Linear approximation of transfer function with a pole of fractional power. IEEE Trans. Automat. Control, 29: 441-444.
    • (1984) IEEE Trans. Automat. Control , vol.29 , pp. 441-444
    • Sun, H.H.1    Abdelwahab, A.A.2    Onaral, B.3
  • 30
    • 57349141862 scopus 로고    scopus 로고
    • On the numerical solution of neutral delay differential equations using multiquadric approximation scheme
    • Vanani, S.K. and A. Aminataei, 2008. On the numerical solution of neutral delay differential equations using multiquadric approximation scheme. Bull. Korean Math. Soc., 45: 663-670.
    • (2008) Bull. Korean Math. Soc. , vol.45 , pp. 663-670
    • Vanani, S.K.1    Aminataei, A.2
  • 31
    • 55549132926 scopus 로고    scopus 로고
    • Multiquadric approximation scheme on the numerical solution of delay differential systems of neutral type
    • Vanani, S.K. and A. Aminataei, 2009. Multiquadric approximation scheme on the numerical solution of delay differential systems of neutral type. Math. Comput. Modell., 49: 234-241.
    • (2009) Math. Comput. Modell. , vol.49 , pp. 234-241
    • Vanani, S.K.1    Aminataei, A.2
  • 32
    • 79960988872 scopus 로고    scopus 로고
    • Tau approximate solution of fractional partial differential equations
    • Vanani, S.K. and A. Aminataei, 2011. Tau approximate solution of fractional partial differential equations. Comput. Math. Appl., 62: 1075-1083.
    • (2011) Comput. Math. Appl. , vol.62 , pp. 1075-1083
    • Vanani, S.K.1    Aminataei, A.2
  • 33
    • 78751609147 scopus 로고    scopus 로고
    • Numerical solution of differential algebraic equations using multiquadric approximation scheme
    • Vanani, S.K. and A. Aminataei, 2011. Numerical solution of differential algebraic equations using multiquadric approximation scheme. Math. Comput. Modell., 53: 659-666.
    • (2011) Math. Comput. Modell. , vol.53 , pp. 659-666
    • Vanani, S.K.1    Aminataei, A.2
  • 34
    • 0032529187 scopus 로고    scopus 로고
    • A numerical method for heat transfer problems using collocation and radial basis functions
    • Zerroukut, M., H. Power and C.S. Chen, 1998. A numerical method for heat transfer problems using collocation and radial basis functions. Int. J. Numer. Math. Eng., 42: 1263-1278.
    • (1998) Int. J. Numer. Math. Eng. , vol.42 , pp. 1263-1278
    • Zerroukut, M.1    Power, H.2    Chen, C.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.