Solving a System of Nonlinear Functional Equations Using Revised New Iterative Method
In the present paper, we present a modification of the
New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari
[J. Math. Anal. Appl. 2006;316:753–763] and use it for solving
systems of nonlinear functional equations. This modification yields
a series with faster convergence. Illustrative examples are presented
to demonstrate the method.
[1] I. Podlubny, Fractional Differential Equations, Academic Press, San
Diego, 1999.
[2] L. Debnath, Int. J. Math. and Math. Sci., 2003, 1(2003)
[3] G. Adomian, Solving Frontier Problems of Physics: The Decomposition
Method, Kluwer, 1994.
[4] J. H. He, Comput. Meth. Appl. Mech. Eng., 167, 57(1998)
[5] J. H. He, Comput. Meth. Appl. Mech. Eng., 178, 257(1999)
[6] V. Daftardar-Gejji, H. Jafari, J. Math. Anal. Appl., 316, 753(2006)
[7] S. Bhalekar, V. Daftardar-Gejji, Solving Riccati differential equations
of fractional order using the new iterative method, (submitted for
publication).
[8] S. Bhalekar, V. Daftardar-Gejji, New Iterative Method: Application to
Partial Differential Equations, (submitted for publication).
[9] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and
Derivatives: Theory and Applications, Gordon and Breach, Yverdon,
1993.
[10] H. Jafari, V. Daftardar-Gejji, Appl. Math. Comput., 181, 598(2006)
[11] A. M. Wazwaz, Comput. Math. Appl., 54, 895(2007)
[12] D.D. Ganji, M. Nourollahi, E. Mohseni, Comput. and Math. with Appl.,
(In press), doi:10.1016/j.camwa.2006.12.078.
[1] I. Podlubny, Fractional Differential Equations, Academic Press, San
Diego, 1999.
[2] L. Debnath, Int. J. Math. and Math. Sci., 2003, 1(2003)
[3] G. Adomian, Solving Frontier Problems of Physics: The Decomposition
Method, Kluwer, 1994.
[4] J. H. He, Comput. Meth. Appl. Mech. Eng., 167, 57(1998)
[5] J. H. He, Comput. Meth. Appl. Mech. Eng., 178, 257(1999)
[6] V. Daftardar-Gejji, H. Jafari, J. Math. Anal. Appl., 316, 753(2006)
[7] S. Bhalekar, V. Daftardar-Gejji, Solving Riccati differential equations
of fractional order using the new iterative method, (submitted for
publication).
[8] S. Bhalekar, V. Daftardar-Gejji, New Iterative Method: Application to
Partial Differential Equations, (submitted for publication).
[9] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and
Derivatives: Theory and Applications, Gordon and Breach, Yverdon,
1993.
[10] H. Jafari, V. Daftardar-Gejji, Appl. Math. Comput., 181, 598(2006)
[11] A. M. Wazwaz, Comput. Math. Appl., 54, 895(2007)
[12] D.D. Ganji, M. Nourollahi, E. Mohseni, Comput. and Math. with Appl.,
(In press), doi:10.1016/j.camwa.2006.12.078.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:50349", author = "Sachin Bhalekar and Varsha Daftardar-Gejji", title = "Solving a System of Nonlinear Functional Equations Using Revised New Iterative Method", abstract = "In the present paper, we present a modification of the
New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari
[J. Math. Anal. Appl. 2006;316:753–763] and use it for solving
systems of nonlinear functional equations. This modification yields
a series with faster convergence. Illustrative examples are presented
to demonstrate the method.", keywords = "Caputo fractional derivative, System of nonlinear functional
equations, Revised new iterative method.", volume = "6", number = "8", pages = "834-5", }