Numerıcal Approxımatons for Solvıng Partıal Dıfferentıal Equatıons wıth Varıable Coeffıcıents
Applied and Computational Mathematics
Volume 2, Issue 1, February 2013, Pages: 19-23
Received: Mar. 8, 2013; Published: Feb. 20, 2013
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Author
Veyis TURUT, Department of Mathematics, Faculty of Arts and Sciences, Batman University, Batman,Turkey
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Abstract
In this paper, variational iteration method (VIM) and multivariate padé approximaton (MPA) were compared. First, partial differential eqaution has been solved and converted to power series by variational iteration method (VIM), then the numerical solution of partial differential eqauation was put into multivariate padé series. Thus the numerical solutions of the partial differential eqautions were obtained. Numerical solutions of two examples were calculated and results were presented in tables and figures.
Keywords
Variational Iteration Method (VIM), Multivariate Padé Approximaton (MPA), Partial Differential Equation (Pde)
To cite this article
Veyis TURUT, Numerıcal Approxımatons for Solvıng Partıal Dıfferentıal Equatıons wıth Varıable Coeffıcıents, Applied and Computational Mathematics. Vol. 2, No. 1, 2013, pp. 19-23. doi: 10.11648/j.acm.20130201.13
References
[1]
G. Adomian, A review of the decomposition method in applied mathematics, J Math Anal Appl (1988), 135: 501–544.
[2]
A. M. Wazwaz, A reliable modification of Adomian decom-position method, Appl Math Comput (1999), 102: 77–86.
[3]
I. H. Abdel-Halim Hassan, Comparison differential trans-formation technique with Adomian decomposition method for linear and nonlinear initial value problems, Chaos Solitons Fractals (2008), 36: 53–65.
[4]
N. Bildik, H. Bayramoglu, The solution of two dimensional nonlinear differential equation by the Adomian decomposition method, Applied Mathematics and Computation (2005), 163: 519–524.
[5]
J. H. He and X. H.Wu, Variational iteration method: new development and applications, Comput Math Appl (2007), 54: 881–894.
[6]
J. H. He, Variational iteration method—some recent results and new interpretations, J Comput Appl Math (2007), 207: 3–17.
[7]
S. Momani, S. Abuasad, and Z. Odibat, Variational iteration method for solving nonlinear boundary value problems, Appl Math Comput (2006), 183: 1351–1358.
[8]
A. Yıldırım and T. Öziş, Solutions of Singular IVPs of Lane-Emden type by the variational iteration method, Nonlinear Analysis Ser A: Theory Methods Appl (2009), 70: 2480–2484.
[9]
F. Ayaz, Solutions of the System of Differential Equations by Differential Transform Method, Applied Mathematics and Computation (2004) , 147:547-567.
[10]
N. Bildik, A. Konuralp, F. Bek, S. Kucukarslan, Solution of different type of the partial differential equation by differential transform method and Adomian’s decomposition method, Appl. Math. Comput. (2006), 172: 551–567.
[11]
V. Turut, E. Çelik, M. Yiğider, Multivariate padé approxi-mation for solving partial differential equations (PDE), In-ternational Journal For Numerical Methods In Fluids (2011), 66 (9): 1159–1173.
[12]
V. Turut, N. Güzel, Multivariate padé approximation for solving partial differential equations of fractional order, Ab-stract and Applied Analysis (2013), in press.
[13]
V. Turut, N. Güzel, Comparing Numerical Methods for Solving Time-Fractional Reaction-Diffusion Equations, ISRN Mathematical Analysis (2012), doi:10.5402/2012/737206.
[14]
V. Turut,’’ Application of Multivariate padé approximation for partial differential equations’’ , Batman University Journal of Life Sciences (2012), (accepted).
[15]
Ph. Guillaume, A. Huard, Multivariate Padé Approximants, Journal of Computational and Applied Mathematics (2000), 121:197-219.
[16]
J.H. He, A new approach to nonlinear partial differential equations. Communications in Nonlinear Science and Nu-merical Simulation (1997), 2: 230–235.
[17]
J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput Method Appl Mech Eng (1998), 167: 57–68.
[18]
Ph. Guillaume, Nested Multivariate Padé Approximants, J. Comput. Appl. Math. (1997) 82:149-158.
[19]
J. H. He, Variational iteration method a kind of nonlinear analytical technique: some examples, Internat J Nonlinear Mech (1999), 34: 699–708.
[20]
J. H. He, Variational iteration method for autonomous ordi-nary differential systems, Appl Math Comput (2000), 114 : 115–123.
[21]
J. H. He, Some asymptotic methods for strongly nonlinear equations. Int J Mod Phys B (2006), 20: 1141–99.
[22]
J. H. He, Wu XH, Construction of solitary solution and compact on-like solution by variational iteration method. Chaos, Solitons & Fractals (2006), 29: 108–13.
[23]
J.H. He, Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, So-litons & Fractals (2004), 19: 847–51.
[24]
A. Cuyt, L. Wuytack, Nonlinear Methods in Numerical Analysis, Elsevier Science Publishers B.V. (1987), Amster-dam.
[25]
A.H.A. Ali, K.R. Raslan, Variational iterasyon method for solving partial differential eqauations with variable coeffi-cients, chaos, Solitons and Fractals (2009), 40:1520-1529.
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