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Convergence of the variational iteration method for solving multi-delay differential equations. (English) Zbl 1219.65086
Summary: This paper employs the variational iteration method (VIM) to obtain analytical solutions of multi-delay differential equations. Some convergence results are given, and an effective technique for choosing a reasonable initial solution is designed in the solving process; an example is given to elucidate it.
MSC:
65L99Numerical methods for ODE
65L03Functional-differential equations (numerical methods)
References:
[1]He, J. H.: A new approach to linear partial differential equations, Commun. nonlinear sci. Numer. simul. 2, No. 4, 230-235 (1997) · Zbl 0923.35046 · doi:10.1016/S1007-5704(97)90029-0
[2]He, J. H.: Some applications of nonlinear fractional differential equations and their approximations, Bull. sci. Technol. 15, No. 12, 86-90 (1999)
[3]He, J. H.: Variational iteration method for delay differential equations, Commun. nonlinear sci. Numer. simul. 2, No. 4, 235-236 (1997) · Zbl 0924.34063
[4]Tatari, Mehdi; Dehghan, Mehdi: On the convergence of he’s variational iteration method, J. comput. Appl. math. 207, 121-128 (2007) · Zbl 1120.65112 · doi:10.1016/j.cam.2006.07.017
[5]Abdou, M. A.; Soliman, A. A.: Variational iteration method for solving burger’s and coupled burger’s equations, J. comput. Appl. math. 181, 245-251 (2005) · Zbl 1072.65127 · doi:10.1016/j.cam.2004.11.032
[6]Batiha, B.; Noorani, M. S. M.; Hashim, I.; Ismail, E. S.: The multiple stage variational iteration method for class of nonlinear system of odes, Phys. scr. 76, 388-392 (2007) · Zbl 1132.34008 · doi:10.1088/0031-8949/76/4/018
[7]Darvishi, M. T.; Khani, F.; Soliman, A. A.: The numerical simulation for stiff systems of ordinary differential equations, Computers math. Appl. 54, 1055-1063 (2007) · Zbl 1141.65371 · doi:10.1016/j.camwa.2006.12.072
[8]Salkuyeh, Davod Khojasteh: Convergence of the variational iteration method for solving linear systems of odes with constant coefficients, Comput. math. Appl. 56, 2027-2033 (2008) · Zbl 1165.65376 · doi:10.1016/j.camwa.2008.03.030
[9]Yu, Zhan-Hua: Variational iteration method for solving the multi-pantograph delay equation, Phys. lett. A. 372, 6475-6479 (2008) · Zbl 1225.34024 · doi:10.1016/j.physleta.2008.09.013
[10]Mokhtari, R.; Mohammadi, M.: Some remarks on the variational iteration method, Int. J. Nonlinear sci. Numer. simul. 10, 67-74 (2009)