The Differential Transform Method For Solving one-dimensional Burger's Equation and K(m,p,1) Equation

In this paper, a differential transform method (DTM) has been applied to solve one-dimensional Burger's and K(m,p,1) equations with initial conditions and exact solutions have been obtained as same as [1-5]. The results show that DTM has got many merits and much more advantages and it is also a powerful mathematical tool for solving partial differential equations having wide applications in engineering and physics.

Keywords:

Two-dimensional differential transform method, one-dimensional Burger’sequation, K(2, 2, 1) equation, K(3, 3 1) equation.,

PDF

___

Gorguis., A., Appl. Math. Comput. 173 (2006) 126.
Abdou., M. A., Soliman.,A. A.,J. Comput. Appl Math,.181 (2005) 245.
Kaya., D., Appl. Math. Comput. 144 (2003) 353.
Zhu., Y., Tong. K., Chaolu. T., Choas,Soliton & Fractals, 33 (2007) 1411.
Mustafa Inc., Nonlinear Analysis., 69 (2008) 624.
Ablowitz., M. J., Clakson, P. A., Soliton, Nonlinear Evolution Equation and Inverse Scattering, Cambridge University Press, New York, 1991.
Hirota., R., Phys. Rev. Lett. 27 (1971) 1192.
Miurs., M. R. Backlund Transformation, Springer, Berlin,1978.
Weiss., J., Tabor, G., Carnevale, G., J. Math. Phys. 24 (1983) 522.
Yan., C., Phys. Lett. A., 224 (1996) 77.
Wang., M. L., Phys. Lett. A., 213 (1996) 279.
He., J. H., Choas,Soliton & Fractals, 26 (2006) 665.
He., J. H., Phys. Lett. A., 335 (2005) 182.
He., J. H., Int. J. Mod. Phys. B., 10 (2006) 1141
He., J. H., Non-perturbative methods for strongly nonlinear problmi Dissertation, De-Verlag im Internet GmbH, Berlin, 2006.
Abassy., T. A., El-Tawil, M. A., Saleh, Int. J. NonlinearSci. Numer. Simul. 5 (2004) 3
Zhang., S., Xia., T. C., Commun. Theor. Phys (Beijing, China) 46 (2006) 85. Liu.,S. K., Fu, Z. T., Liu., S. D., Zhao., Q., Phys. Lett. A., 289 (2001) 69.
Zhou., Y. B., Wang., M. L., Wang., Y. M., Phys. Lett. A., 308 (2003) 31
Chen.,Y., Yan., Z. Y., Appl. Math. Comput. 177 (2006) 85.
Pukhov., G.E., Differential transformations and mathematical modelling of physical processes, Kiev, 1986
Do˘ gan., N., Ert¨ urk., V. S., Momani., S., Akın., ¨ O., Yıldırım., A., Journal of King Saud University, 23 (2011) 223.
Chen., C.K., Ho, S.H., Appl. Math. Comput. 106 (1999) 171.
Bert., C.W., J. Heat. Transfer, 124 (2002) 208.
Chen., C.L., Yeh, W.Z., Jang, M.J., Appl. Simulation and Modelling, 28-30 (2004) 4
Liu., H., Song, Y., Appl. Math. Comput. 184 (2007) 748.
Abdel- Halim Hassan, I.H., Choas,Soliton & Fractals, 36 (2) (2006) 53.
Figen Kangalgil, Fatma Ayaz, Choas,Soliton & Fractals.,41 (2009) 464.
Figen Kangalgil, Fatma Ayaz, AJSE, 35 (2010) 203.
Figen Kangalgil, Fatma Ayaz, Selcuk. J. Appl. Math. , 8 (2007) 75.
Kurnaz, A., Oturan¸ c, G., Int. J. Comput. Math., 82 (2005) 369.
Ayaz., F., Appl. Math. Comput. 143 (2003) 361.
Ayaz., F., Appl. Math. Comput. 147 (2004) 547. 40