Application of Reduced Differential Transformation Method for Solving Fourth-order Parabolic Partial Differential Equations
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Authors
Birol Ibis
- Department of Main Sciences, Turkish Air Force Academy, 34149 Yeşilyurt, İstanbul, Turkey.
Abstract
The purpose of this paper is to obtain the approximate solution of fourth-order parabolic partial differential equations by the reduced differential transform method (RDTM).This method provides the solution in the form of a convergent series with easily calculable terms. Comparing RDTM with some other methods in the literature shows present approach is very simple, effective, powerful and can be easily applied to other linear or nonlinear PDEs in science and engineering.
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ISRP Style
Birol Ibis, Application of Reduced Differential Transformation Method for Solving Fourth-order Parabolic Partial Differential Equations, Journal of Mathematics and Computer Science, 12 (2014), no. 2, 124-131
AMA Style
Ibis Birol, Application of Reduced Differential Transformation Method for Solving Fourth-order Parabolic Partial Differential Equations. J Math Comput SCI-JM. (2014); 12(2):124-131
Chicago/Turabian Style
Ibis, Birol. "Application of Reduced Differential Transformation Method for Solving Fourth-order Parabolic Partial Differential Equations." Journal of Mathematics and Computer Science, 12, no. 2 (2014): 124-131
Keywords
- Reduced differential transform method (RDTM)
- differential transform method (DTM) fourth-order parabolic partial differential equations
- initial value problems.
MSC
References
-
[1]
A. Q. M. Khaliq, E. H. Twizell, A family of second-order methods for variable coefficient fourth-order parabolic partial differential equations, Int. J. Comput. Math., 23 (1987), 63–76.
-
[2]
D. J. Gorman, Free Vibrations Analysis of Beams and Shafts, Wiley, New York (1975)
-
[3]
C. Andrade, S. McKee, High frequency A.D.I. methods for fourth-order parabolic equations with variable coefficients, Int. J. Comput. Appl. Math., 3 (1977), 11–14.
-
[4]
S. D. Conte, A stable implicit difference approximation to a fourth-order parabolic equation, J. Assoc. Comp. Mach., 4 (1957), 18-23
-
[5]
S. D. Conte, W. C. Royster, Convergence of finite difference solution to a solution of the equation of a vibration beam, Proc. Amer. Math. Soc., 7 (1956), 742–749.
-
[6]
D. J. Evans, A stable explicit method for the finite difference solution of fourth-order parabolic partial differential equations, Comp. J., 8 (1965), 280–287.
-
[7]
D. J. Evans, W. S. Yousef, A note on solving the fourth-order parabolic equation by a AGE method, Int. J. Comput. Math., 40 (1991), 93–97.
-
[8]
K. Arshad, K. Islam, A. Tariq, Sextic spline solution for solving a fourth-order parabolic partial differential equation, Int. J. Comput. Math., 82 (2005), 871-879.
-
[9]
B. K. Belinda, S. Oliver, W. Michael , A fourth-order parabolic equation modeling epitaxial thin film growth, J. Math. Anal. Appl., 286 (2003), 459-490.
-
[10]
Y. L. You, M. Kaveh, Fourth-order partial differential equations for noise removal, IEEE Trans. Image Process, 9 (2000), 1723-1730.
-
[11]
X. H. Tang, C. I. Christov, Non-linear waves of the steady natural convection in a vertical fluid layer: A numerical approach, Math. Comput. Simul, 74 (2007), 203-213.
-
[12]
M. Khan, M. A. Gondal, S. Kumar, A new analytical approach to solve exponential stretching sheet problem in fluid mechanics by variational iterative Pade method, The Journal of Mathematics and Computer Science (JMCS), 3(2) (2011), 135 – 144.
-
[13]
A. M. Wazwaz, Analytical treatment for variable coefficients fourth-order parabolic partial differential equations, Appl. Math. and Comput., 123 (2001), 219-227.
-
[14]
A. M. Wazwaz, Exact solutions for variable coefficients fourth-order parabolic partial differential equations in higher-dimensional spaces, Appl. Math. and Comput., 130 (2002), 415-424.
-
[15]
M. A. Noor, K. I. Noor, S. T. Mohyud-Din, Modified variational iteration technique for solving singular fourth-order parabolic partial differential equations, Nonlinear Anal-Theor, 71(12) (2009), 630-640.
-
[16]
J. Biazar, H. Ghazvini, He’s variational iteration method for fourth-order parabolic equations, Comput. & Math. with Appl., 54(7-8) (2007), 1047-1054.
-
[17]
R. C. Mittal, R. K. Jain, B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equations, Appl. Math. and Comput., 217(23) (2011), 9741-9755.
-
[18]
H. Caglar, N. Caglar, Fifth-degree B-spline solution for a fourth-order parabolic partial differential equations , Appl. Math. and Comput, 201(1-2) (2008), 597-603.
-
[19]
T. Aziz, A. Khan, J. Rashidinia, Spline methods for the solution of fourth-order parabolic partial differential equations, Appl. Math. and Comput, 167(1) (2005), 153-166.
-
[20]
J. Biazar, H. Ghazvini , Convergence of the homotopy perturbation method for partial differential equations, Nonlinear Anal. Real World Appl., 10(5) (2009), 2633-2640.
-
[21]
M. Matinfar, M. Saeidy, Application of Homotopy analysis method to fourth-order parabolic partial differential equations, Appl. Appl. Math.: An Int. J. (AAM), 5(1) (2010), 70- 80.
-
[22]
Y. Keskin, G. Oturanç, Reduced differential transform method for partial differential equations, Int J. Nonlinear Sci. Numer. Simul, 10(6) (2009), 741–9.
-
[23]
P. K. Gupta , Approximate analytical solutions of fractional Benney–Lin equation by reduced differential transform method and the homotopy perturbation method, Comput. Math. Appl., 61(9) (2011), 2829-2842.
-
[24]
R. Abazari, M. Abazari, Numerical simulation of generalized Hirota–Satsuma coupled KdV equation by RDTM and comparison with DTM, Commun. Nonlinear Sci. Numer. Simul, 17(2) (2012), 619-629.
-
[25]
K. Yıldırım, B. İbiş, M. Bayram, New solutions of the non linear Fisher type equations by the reduced differential transform , Nonlinear Sci. Lett. A, 3 (1) (2012), 29-36.
-
[26]
A. Haghbin, S. Hesam, Reduced Differential Transform Method For Solving Seventh Order Sawada Kotera Equations, The Journal of Mathematics and Computer Science (JMCS), 5 (1) (2012), 53-59.