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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:
65L99 Numerical methods for ordinary differential equations
65L03 Numerical methods for functional-differential equations
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[1] He, J.H., A new approach to linear partial differential equations, Commun. nonlinear sci. numer. simul., 2, 4, 230-235, (1997)
[2] He, J.H., Some applications of nonlinear fractional differential equations and their approximations, Bull. sci. technol., 15, 12, 86-90, (1999)
[3] He, J.H., Variational iteration method for delay differential equations, Commun. nonlinear sci. numer. simul., 2, 4, 235-236, (1997)
[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
[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
[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
[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
[8] Khojasteh Salkuyeh, Davod, 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
[9] Yu, Zhan-Hua, Variational iteration method for solving the multi-pantograph delay equation, Phys. lett. A., 372, 6475-6479, (2008) · Zbl 1225.34024
[10] Mokhtari, R.; Mohammadi, M., Some remarks on the variational iteration method, Int. J. nonlinear sci. numer. simul., 10, 67-74, (2009)
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