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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access November 24, 2015

Multivariate Padé Approximations For Solving Nonlinear Diffusion Equations

V. Turut
From the journal Open Physics

Abstract

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.

References

[1] E.Celik, E. Karaduman and M. Bayram, Numerical Solutions of Chemical Differential- Algebraic Equations, Applied Mathematics and Computation (2003),139 (2-3),259-264. 10.1016/S0096-3003(02)00178-9Search in Google Scholar

[2] E. Celik, M. Bayram, Numerical solution of differential–algebraic equation systems and applications, Applied Mathematics and Computation (2004), 154 (2) 405-413. 10.1016/S0096-3003(03)00719-7Search in Google Scholar

[3] V. Turut and N Guzel., Comparing Numerical Methods for Solving Time-Fractional Reaction-Diffusion Equations, ISRNMathematical Analysis (2012), Doi:10.5402/2012/737206. 10.5402/2012/737206Search in Google Scholar

[4] V. Turut, N. Güzel, Multivariate Padé approximation for solving partial differential equations of fractional order”,Abstract and Applied Analysis (2013), Doi:10.1155/2013/746401. 10.1155/2013/746401Search in Google Scholar

[5] V. Turut, E. Çelik, M. Yiğider, Multivariate Padé approximation for solving partial differential equations (PDE), International Journal For Numerical Methods In Fluids (2011), 66(9):1159-1173. 10.1002/fld.2305Search in Google Scholar

[6] V. Turut,” Application of Multivariate Padé approximation for partial differential equations”,Batman University Journal of Life Sciences (2012), 2(1): 17–28. 10.1155/2013/746401Search in Google Scholar

[7] V. Turut,” Numerical approximations for solving partial differential equations with variable coeflcients” Applied and Computational Mathematics. (2013), 2 (1),19-23 Search in Google Scholar

[8] A. Sadighi, D.D. Ganji, Exact solutions of nonlinear diffusion equations by variational iteration method, Computers Mathematics with Applications (2007), 54: 1112-1121. 10.1016/j.camwa.2006.12.077Search in Google Scholar

[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. 10.1016/S0045-7825(98)00108-XSearch in Google Scholar

[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. 10.1016/S0020-7462(98)00048-1Search in Google Scholar

[11] J.H. He, Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math. (2007), 207: 3-17. 10.1016/j.cam.2006.07.009Search in Google Scholar

[12] J.H. He, X.H. Wu, Variational iteration method: new development and applications, Comput. Math. Appl. (2007), 54: 881-894. 10.1016/j.camwa.2006.12.083Search in Google Scholar

[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. Search in Google Scholar

[14] A. Cuyt, L. Wuytack, Nonlinear Methods in Numerical Analysis, Elsevier Science Publishers B.V. (1987), Amsterdam. Search in Google Scholar

[15] A.M. Wazwaz, Exact solutions to nonlinear diffusion equations obtained by the decomposition method, Applied Mathematics and Computation, (2001), 109-122. 10.1016/S0096-3003(00)00064-3Search in Google Scholar

[16] Ph. Guillaume, A. Huard, Multivariate Padé Approximants, Journal of Computational and Applied Mathematics, (2000), 121: 197-219. 10.1016/S0377-0427(00)00337-XSearch in Google Scholar

[17] J.S.R. Chisholm, Rational approximants defined from double power series, Math. Comp. (1973) 27: 841-848. 10.1090/S0025-5718-1973-0382928-6Search in Google Scholar

[18] D. Levin, General order Padé-type rational approximants defined from double power series, J. Inst. Math. Appl. (1976) 18: 395-407. 10.1093/imamat/18.1.1Search in Google Scholar

[19] A. Cuyt, Multivariate Padé approximants, J. Math. Anal. Appl. (1983) 96: 283-293. 10.1016/0022-247X(83)90041-0Search in Google Scholar

[20] A. Cuyt, A Montessus de Ballore Theorem for Multivariate Padé Approximants, J. Approx. Theory (1985) 43: 43-52. 10.1016/0021-9045(85)90147-9Search in Google Scholar

Received: 2015-9-2
Accepted: 2015-10-27
Published Online: 2015-11-24

©2015 V. Turut

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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