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Number of results

Journal

2015 | 13 | 1 |

Article title

Multivariate Padé Approximations For Solving
Nonlinear Diffusion Equations

Authors

Content

Title variants

Languages of publication

EN

Abstracts

EN
In this paper, multivariate Padé approximation
is applied to power series solutions of nonlinear diffusion
equations. As it is seen from tables, multivariate Padé approximation
(MPA) gives reliable solutions and numerical
results.

Publisher

Journal

Year

Volume

13

Issue

1

Physical description

Dates

received
2 - 9 - 2015
online
24 - 11 - 2015
accepted
27 - 10 - 2015

Contributors

author
  • Department of Mathematics,
    Faculty of Science and Letters, Batman University, 72060 - Batman,
    Turkey

References

  • [1] E.Celik, E. Karaduman and M. Bayram, Numerical Solutions of Chemical Differential- Algebraic Equations, Applied Mathematics andComputation (2003),139 (2-3),259-264.
  • [2] E. Celik, M. Bayram, Numerical solution of differential–algebraic equation systems and applications, Applied Mathematics and Computation(2004), 154 (2) 405-413.
  • [3] V. Turut and N Guzel., Comparing Numerical Methods for Solving Time-Fractional Reaction-Diffusion Equations, ISRNMathematical Analysis(2012), Doi:10.5402/2012/737206.[Crossref]
  • [4] V. Turut, N. Güzel, Multivariate Padé approximation for solving partial differential equations of fractional order”,Abstract and AppliedAnalysis (2013), Doi:10.1155/2013/746401.[Crossref]
  • [5] V. Turut, E. Çelik, M. Yiğider, Multivariate Padé approximation for solving partial differential equations (PDE), International Journal ForNumerical Methods In Fluids (2011), 66(9):1159-1173.
  • [6] V. Turut,” Application of Multivariate Padé approximation for partial differential equations”,Batman University Journal of Life Sciences(2012), 2(1): 17–28.
  • [7] V. Turut,” Numerical approximations for solving partial differential equations with variable coeflcients” Applied and ComputationalMathematics. (2013), 2 (1),19-23
  • [8] A. Sadighi, D.D. Ganji, Exact solutions of nonlinear diffusion equations by variational iteration method, Computers Mathematics withApplications (2007), 54: 1112-1121.
  • [9] J.H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Eng.(1998), 167: 57-68.
  • [10] J.H. He, Variational iteration method-a kind of non-linear analytical technique: some examples, Int. J. Non-Linear. Mech. (1999), 34:699-708.
  • [11] J.H. He, Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math. (2007), 207: 3-17.[WoS]
  • [12] J.H. He, X.H. Wu, Variational iteration method: new development and applications, Comput. Math. Appl. (2007), 54: 881-894.[WoS]
  • [13] J.H. He, G.-C. Wu, F. Austin, The variational iteration method which should be followed, Nonlinear Sci. Lett. A (2010), 1: 1-30.
  • [14] A. Cuyt, L. Wuytack, Nonlinear Methods in Numerical Analysis, Elsevier Science Publishers B.V. (1987), Amsterdam.
  • [15] A.M. Wazwaz, Exact solutions to nonlinear diffusion equations obtained by the decomposition method, Applied Mathematics and Computation,(2001), 109-122.[Crossref]
  • [16] Ph. Guillaume, A. Huard, Multivariate Padé Approximants, Journal of Computational and Applied Mathematics, (2000), 121: 197-219.
  • [17] J.S.R. Chisholm, Rational approximants defined from double power series, Math. Comp. (1973) 27: 841-848.[Crossref]
  • [18] D. Levin, General order Padé-type rational approximants defined from double power series, J. Inst. Math. Appl. (1976) 18: 395-407.[Crossref]
  • [19] A. Cuyt, Multivariate Padé approximants, J. Math. Anal. Appl. (1983) 96: 283-293.[Crossref]
  • [20] A. Cuyt, A Montessus de Ballore Theorem for Multivariate Padé Approximants, J. Approx. Theory (1985) 43: 43-52.[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_1515_phys-2015-0041
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