Solution of initial and boundary value problems by the variational iteration method

Date

2014-03-15

Author

Altintan, D.
Uğur, Ömür

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The Variational Iteration Method (VIM) is an iterative method that obtains the approximate solution of differential equations. In this paper, it is proven that whenever the initial approximation satisfies the initial conditions, vim obtains the solution of Initial Value Problems (IVPs) with a single iteration. By using this fact, we propose a new algorithm for Boundary Value Problems (BVPs): linear and nonlinear ones. Main advantage of the present method is that it does not use Green's function, however, it has the same effect that it produces the exact solution to linear problems within a single, but simpler, integral. In order to show the effectiveness of the method we give some examples including linear and nonlinear BVPs.

Subject Keywords

Variational iteration method, Initial value problems, Boundary value problems, Green's function

URI

https://hdl.handle.net/11511/32157

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2013.07.012

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

D. Altintan and Ö. Uğur, “Solution of initial and boundary value problems by the variational iteration method,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 790–797, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32157.