Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations
Affiliation(s)
Department of Mathematics, University of Vlora, Vlora, Albania. Department of Mathematics, Polytechnic University of Tirana, Tirana, Albania.
Department of Mathematics, University of Vlora, Vlora, Albania. Department of Mathematics, Polytechnic University of Tirana, Tirana, Albania.
ABSTRACT
In this paper, we present a new method, a mixture of homotopy perturbation method and a new integral transform to solve some nonlinear partial differential equations. The proposed method introduces also He’s polynomials [1]. The analytical results of examples are calculated in terms of convergent series with easily computed components [2].
Cite this paper
A. Kashuri, A. Fundo and M. Kreku, "Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations," Advances in Pure Mathematics, Vol. 3 No. 3, 2013, pp. 317-323. doi: 10.4236/apm.2013.33045.
A. Kashuri, A. Fundo and M. Kreku, "Mixture of a New Integral Transform and Homotopy Perturbation Method for Solving Nonlinear Partial Differential Equations," Advances in Pure Mathematics, Vol. 3 No. 3, 2013, pp. 317-323. doi: 10.4236/apm.2013.33045.
References
[1] E. M. E. Zayed and H. M. Abdel Rahman, “On Using the He’s Polynomials for Solving the Nonlinear Coupled Evolution Equations in Mathematical Physics,” WSEAS Transactions on Mathematics, Vol. 11, No. 4, 2012, pp. 294-302. [2] D. Kumar, J. Singh and S. Rathore, “Sumudu Decomposition Method for Nonlinear Equations,” International Mathematical Forum, Vol. 7, No. 11, 2012, pp. 515-521. [3] A. Kashuri and A. Fundo, “A New Integral Transform,” Advances in Theoretical and Applied Mathematics, Vol. 8, No. 1, 2013, pp. 27-43. [4] R. K. Nagle, E. B. Saff and A. D. Snider, “Fundamentals of Differential Equations,” 8th Edition, Pearson, London, 2011, p. 367. [5] T. M. Elzaki and E. M. A. Hilal, “Homotopy Perturbation and Elzaki Transform for Solving Nonlinear Partial Differential Equations,” Mathematical Theory and Modeling, Vol. 2, No. 3, 2012, pp. 33-43.
[1] E. M. E. Zayed and H. M. Abdel Rahman, “On Using the He’s Polynomials for Solving the Nonlinear Coupled Evolution Equations in Mathematical Physics,” WSEAS Transactions on Mathematics, Vol. 11, No. 4, 2012, pp. 294-302. [2] D. Kumar, J. Singh and S. Rathore, “Sumudu Decomposition Method for Nonlinear Equations,” International Mathematical Forum, Vol. 7, No. 11, 2012, pp. 515-521. [3] A. Kashuri and A. Fundo, “A New Integral Transform,” Advances in Theoretical and Applied Mathematics, Vol. 8, No. 1, 2013, pp. 27-43. [4] R. K. Nagle, E. B. Saff and A. D. Snider, “Fundamentals of Differential Equations,” 8th Edition, Pearson, London, 2011, p. 367. [5] T. M. Elzaki and E. M. A. Hilal, “Homotopy Perturbation and Elzaki Transform for Solving Nonlinear Partial Differential Equations,” Mathematical Theory and Modeling, Vol. 2, No. 3, 2012, pp. 33-43.