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Zbl 1245.65088
Khader, M.M.
Introducing an efficient modification of the variational iteration method by using Chebyshev polynomials. (English)
[J] Appl. Appl. Math. 7, No. 1, 283-299, electronic only (2012). ISSN 1932-9466/e

Summary: An efficient modification of the variational iteration method is presented using Chebyshev polynomials. Special attention is given to study the convergence of the proposed method. The new modification is tested for some examples to demonstrate reliability and efficiency of the proposed method. A comparison of our numerical results those of the conventional numerical method, the fourth-order Runge-Kutta method are given. The comparison shows that the solution using our modification is fast-convergent and is in excellent conformance with the exact solution. Finally, we conclude that the proposed method can be applied to a large class of linear and non-linear differential equations.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65L05 Initial value problems for ODE (numerical methods)

Keywords: variational iteration method; Chebyshev polynomials; convergence; fourth-order Runge-Kutta method; numerical results

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Zentralblatt MATH Berlin [Germany]