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Convergence of the new iterative method. (English) Zbl 1239.34014
Summary: A new iterative method introduced by {\it V. Daftardar-Gejji} and {\it H. Jafari} [J. Math. Anal. Appl. 316, No. 2, 753--763 (2006; Zbl 1087.65055)] is an efficient technique to solve nonlinear functional equations. In the present paper, sufficiency conditions for convergence of DJM are presented. Further equivalence of DJM and Adomian decomposition method is established.

MSC:
34A45Theoretical approximation of solutions of ODE
35A35Theoretical approximation to solutions of PDE
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References:
[1] G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, vol. 60 of Fundamental Theories of Physics, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1994. · Zbl 0843.34026
[2] G. Adomian, “A review of the decomposition method in applied mathematics,” Journal of Mathematical Analysis and Applications, vol. 135, no. 2, pp. 501-544, 1988. · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9
[3] V. Daftardar-Gejji and H. Jafari, “Adomian decomposition: a tool for solving a system of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 301, no. 2, pp. 508-518, 2005. · Zbl 1061.34003 · doi:10.1016/j.jmaa.2004.07.039
[4] Y. Cherruault, “Convergence of Adomian’s method,” Kybernetes, vol. 18, no. 2, pp. 31-38, 1989. · Zbl 0697.65051 · doi:10.1108/eb005812
[5] K. Abbaoui and Y. Cherruault, “New ideas for proving convergence of decomposition methods,” Computers & Mathematics with Applications, vol. 29, no. 7, pp. 103-108, 1995. · Zbl 0832.47051 · doi:10.1016/0898-1221(95)00022-Q
[6] H.-W. Choi and J.-G. Shin, “Symbolic implementation of the algorithm for calculating Adomian polynomials,” Applied Mathematics and Computation, vol. 146, no. 1, pp. 257-271, 2003. · Zbl 1033.65036 · doi:10.1016/S0096-3003(02)00541-6
[7] H. Jafari and V. Daftardar-Gejji, “Solving a system of nonlinear fractional differential equations using Adomian decomposition,” Journal of Computational and Applied Mathematics, vol. 196, no. 2, pp. 644-651, 2006. · Zbl 1099.65137 · doi:10.1016/j.cam.2005.10.017
[8] V. Daftardar-Gejji and H. Jafari, “An iterative method for solving nonlinear functional equations,” Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp. 753-763, 2006. · Zbl 1087.65055 · doi:10.1016/j.jmaa.2005.05.009
[9] M. C. Joshi and R. K. Bose, Some Topics in Nonlinear Functional Analysis, A Halsted Press Book, John Wiley & Sons, New York, NY, USA, 1985. · Zbl 0596.47038
[10] A. A. M. Cuyt, “Padé-approximants in operator theory for the solution of nonlinear differential and integral equations,” Computers & Mathematics with Applications, vol. 8, no. 6, pp. 445-466, 1982. · Zbl 0507.65022 · doi:10.1016/0898-1221(82)90019-0
[11] M. A. Noor and K. I. Noor, “Three-step iterative methods for nonlinear equations,” Applied Mathematics and Computation, vol. 183, no. 1, pp. 322-327, 2006. · Zbl 1113.65050 · doi:10.1016/j.amc.2006.05.055
[12] M. A. Noor, K. I. Noor, S. T. Mohyud-Din, and A. Shabbir, “An iterative method with cubic convergence for nonlinear equations,” Applied Mathematics and Computation, vol. 183, no. 2, pp. 1249-1255, 2006. · Zbl 1113.65052 · doi:10.1016/j.amc.2006.05.133
[13] K. I. Noor and M. A. Noor, “Iterative methods with fourth-order convergence for nonlinear equations,” Applied Mathematics and Computation, vol. 189, no. 1, pp. 221-227, 2007. · Zbl 1300.65029 · doi:10.1016/j.amc.2006.11.080
[14] M. A. Noor, “New iterative schemes for nonlinear equations,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 937-943, 2007. · Zbl 1116.65056 · doi:10.1016/j.amc.2006.09.028
[15] M. A. Noor, K. I. Noor, E. Al-Said, and M. Waseem, “Some new iterative methods for nonlinear equations,” Mathematical Problems in Engineering, vol. 2010, Article ID 198943, 12 pages, 2010. · Zbl 1207.65054 · doi:10.1155/2010/198943 · eudml:223211
[16] S. T. Mohyud-Din, A. Yildirim, and S. M. M. Hosseini, “Numerical comparison of methods for Hirota-Satsuma model,” Applications and Applied Mathematics, vol. 5, no. 10, pp. 1554-1563, 2010. · Zbl 1205.65289 · http://www.pvamu.edu/pages/7187.asp
[17] S. T. M. Din, A. Yildirim, and M. M. Hosseini, “An iterative algorithm for fifth-order boundary value problems,” World Applied Sciences Journal, vol. 8, no. 5, pp. 531-535, 2010.
[18] M. A. Noor and S. T. M. Din, “An iterative method for solving Helmholtz equations,” Arab Journal of Mathematics and Mathematical Sciences, vol. 1, no. 1, pp. 13-18, 2007.
[19] V. Daftardar-Gejji and S. Bhalekar, “Solving fractional diffusion-wave equations using a new iterative method,” Fractional Calculus & Applied Analysis, vol. 11, no. 2, pp. 193-202, 2008. · Zbl 1210.26009 · eudml:11339
[20] V. Daftardar-Gejji and S. Bhalekar, “Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1801-1809, 2010. · Zbl 1189.35357 · doi:10.1016/j.camwa.2009.08.018
[21] S. Bhalekar and V. Daftardar-Gejji, “New iterative method: application to partial differential equations,” Applied Mathematics and Computation, vol. 203, no. 2, pp. 778-783, 2008. · Zbl 1154.65363 · doi:10.1016/j.amc.2008.05.071
[22] V. Daftardar-Gejji and S. Bhalekar, “An Iterative method for solving fractional differential equations,” Proceedings in Applied Mathematics and Mechanics, vol. 7, no. 1, pp. 2050017-2050018, 2008. · Zbl 1210.26009 · doi:10.1002/pamm.200701001
[23] S. Bhalekar and V. Daftardar-Gejji, “Solving evolution equations using a new iterative method,” Numerical Methods for Partial Differential Equations, vol. 26, no. 4, pp. 906-916, 2010. · Zbl 1194.65117 · doi:10.1002/num.20463
[24] H. Jafari, S. Seifi, A. Alipoor, and M. Zabihi, “An Iterative Method for solving linear and nonlinear fractional diffusion-wave equation,” International e-Journal of Numerical Analysis and Related Topics, vol. 3, pp. 20-32, 2009.
[25] O. S. Fard and M. Sanchooli, “Two successive schemes for numerical solution of linear fuzzy Fredholm integral equations of the second kind,” Australian Journal of Basic and Applied Sciences, vol. 4, no. 5, pp. 817-825, 2010.
[26] V. Srivastava and K. N. Rai, “A multi-term fractional diffusion equation for oxygen delivery through a capillary to tissues,” Mathematical and Computer Modelling, vol. 51, no. 5-6, pp. 616-624, 2010. · Zbl 1190.35226 · doi:10.1016/j.mcm.2009.11.002