Abstract
In this manuscript the homotopy perturbation method, the new iterative method, and the variational iterative method have been successively used to obtain approximate analytical solutions of nonlinear Sturm-Liouville, Navier-Stokes and Burgers’ equations. It is shown that the homotopy perturbation method gives approximate analytical solution near to the exact one. We have illustrated the obtained results by sketching the graph of the solutions.
[1] R. Hirota, Phys. Rev. Lett. 27, 1192 (1971) http://dx.doi.org/10.1103/PhysRevLett.27.119210.1103/PhysRevLett.27.1192Search in Google Scholar
[2] C. Rogers, W. K. Schief, Backlund and Darboux transformations (Cambridge University Press, UK, 2002) http://dx.doi.org/10.1017/CBO978051160635910.1017/CBO9780511606359Search in Google Scholar
[3] A.R. Chowdhury, Painleve analysis and its applications (Chapman and Hall/CRC, UK, 2000) Search in Google Scholar
[4] G. Adomian, Solving frontier problems of physics: The decomposition method (Kluwer Academic, Boston, MA, 1994) 10.1007/978-94-015-8289-6Search in Google Scholar
[5] J.H. He, Commun. Nonlin. Sci. Numer. Sim. 2, 230235 (1997) Search in Google Scholar
[6] J.H. He, Comput. Meth. Appl. Mech. Eng. 167, 5768 (1998) Search in Google Scholar
[7] J.H. He, Comput. Meth. Appl. M. 167, 6973 (1998) Search in Google Scholar
[8] J.H. He, Int. J. N. Lin. Mech. 34, 699708 (1999) Search in Google Scholar
[9] J.H. He, Appl. Math. Comput. 114, 123 (2000) http://dx.doi.org/10.1016/S0096-3003(99)00104-610.1016/S0096-3003(99)00104-6Search in Google Scholar
[10] J.H. He, Commun. Nonlin. Sci. Numer. Sim. 2, 236 (1997) Search in Google Scholar
[11] J.H. He, Comput. Meth. Appl. Mech. Eng. 178, 262 (1999) http://dx.doi.org/10.1016/S0045-7825(99)00018-310.1016/S0045-7825(99)00018-3Search in Google Scholar
[12] J.H. He, Appl. Math. Comp. 135, 7379 (2003) Search in Google Scholar
[13] J.H. He, Int. J. N. Lin. Mech. 35, 3743 (2000) Search in Google Scholar
[14] J.H. He, Phys. Lett. A 350, 8788 (2006) http://dx.doi.org/10.1016/j.physleta.2005.10.00510.1016/j.physleta.2005.10.005Search in Google Scholar
[15] S. Abbasbandy, A. Shirzadia, Commun. Nonlin. Sci. Numer. Sim. 16, 112 (2011) http://dx.doi.org/10.1016/j.cnsns.2010.04.00410.1016/j.cnsns.2010.04.004Search in Google Scholar
[16] D. Altintan, O. Ugur, Comput. Math. Appl. 58, 322 (2009) http://dx.doi.org/10.1016/j.camwa.2009.02.02910.1016/j.camwa.2009.02.029Search in Google Scholar
[17] D. Baleanu, Alireza K. Golmankhaneh, A.K. Golmankhaneh, Rom. J. Phys. 54, (2009) Search in Google Scholar
[18] A.K. Golmankhaneha, A.K. Golmankhaneh, D. Baleanu, Signal Proc. 19, 3 (2011) Search in Google Scholar
[19] S. Bhalekar, V. Daftardar-Gejji, Appl. Math. Comput. 203, 778 (2008) http://dx.doi.org/10.1016/j.amc.2008.05.07110.1016/j.amc.2008.05.071Search in Google Scholar
[20] V. Daftardar-Gejji, S. Bhalekar, Comput. Math. Appl. 59, 1801 (2010) http://dx.doi.org/10.1016/j.camwa.2009.08.01810.1016/j.camwa.2009.08.018Search in Google Scholar
[21] M.A. Abdou, A.A. Soliman, Physica D 211, 18 (2005) http://dx.doi.org/10.1016/j.physd.2005.08.00210.1016/j.physd.2005.08.002Search in Google Scholar
[22] M.A. Abdou, A.A. Soliman, J. Comput. Appl. Math. 181, 245 (2005) http://dx.doi.org/10.1016/j.cam.2004.11.03210.1016/j.cam.2004.11.032Search in Google Scholar
[23] S. Momani, S. Abuasad, Chaos 27, 1119 (2006) 10.1016/j.chaos.2005.04.113Search in Google Scholar
[24] H.K. Liu, Appl. Math. Comput. 217, 5259 (2011) http://dx.doi.org/10.1016/j.amc.2010.11.02410.1016/j.amc.2010.11.024Search in Google Scholar
[25] D.D. Ganji, M. Nourollahi, E. Mohseni, Comput. Math. Appl. 54, 1122 (2007) http://dx.doi.org/10.1016/j.camwa.2006.12.07810.1016/j.camwa.2006.12.078Search in Google Scholar
[26] D.D. Ganji, G.A. Afrouzi, R.A. Talarposhti, Phys. Lett. A 368, 450 (2007) http://dx.doi.org/10.1016/j.physleta.2006.12.08610.1016/j.physleta.2006.12.086Search in Google Scholar
[27] E. Hizel, S. Küçükarslan, Nonlin. Anal. Real World Appl. 10, 1932 (2009) http://dx.doi.org/10.1016/j.nonrwa.2008.02.03310.1016/j.nonrwa.2008.02.033Search in Google Scholar
[28] S.J. Liao, Appl. Math. Comput. 147, 499 (2004) http://dx.doi.org/10.1016/S0096-3003(02)00790-710.1016/S0096-3003(02)00790-7Search in Google Scholar
[29] S.J. Liao, Commun. Nonlinear Sci. Numer. Simul. 14, 983 (2009) http://dx.doi.org/10.1016/j.cnsns.2008.04.01310.1016/j.cnsns.2008.04.013Search in Google Scholar
[30] D. Zwillinger, Handbook of Differential Equations, 3rd ed. (Academic Press, Boston, MA, 1997) Search in Google Scholar
[31] J.M. Burgers, Adv. Appl. Mech. 1, 171 (1948) http://dx.doi.org/10.1016/S0065-2156(08)70100-510.1016/S0065-2156(08)70100-5Search in Google Scholar
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