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Introducing an efficient modification of the variational iteration method by using Chebyshev polynomials. (English) Zbl 1245.65088
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:
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
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