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A study on the convergence of variational iteration method. (English) Zbl 1198.65147

Summary: Variational iteration method has been widely used to handle linear and nonlinear models. The main property of the method is its flexibility and ability to solve nonlinear equations accurately and conveniently. In this paper, we present an alternative approach of the method then we study the convergence of the method for nonlinear differential equations. Our emphasis is to address the sufficient condition for convergence and the error estimate. Simple approaches of variational iteration method to nonlinear ordinary, partial and fractional differential equations are presented and the convergence results are briefly discussed. Some examples are investigated to verify convergence results and to illustrate the efficiency of the method. The basic ideas described in this paper are expected to be further employed to handle nonlinear models.

MSC:

65L99 Numerical methods for ordinary differential equations
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