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On the convergence of He’s variational iteration method. (English) Zbl 1120.65112
Summary: We consider J.-H. He’s variational iteration method [Int. J. Mod. Phys. B 20, No. 10, 1141–1199 (2006; Zbl 1102.34039)] for solving second-order initial value problems. We discuss the use of this approach for solving several important partial differential equations. This method is based on the use of Lagrange multipliers for identification of the optimal value of a parameter in a functional. This procedure is a powerful tool for solving the large amount of problems. Using the variational iteration method, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a sequence of functions which converges to the exact solution of the problem. Our emphasis will be on the convergence of the variational iteration method. In the current paper this scheme will be investigated in details and efficiency of the approach will be shown by applying the procedure on several interesting and important models.
65M70Spectral, collocation and related methods (IVP of PDE)
35G25Initial value problems for nonlinear higher-order PDE