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Zbl 1236.65079
Khader, M.M.
Introducing an efficient modification of the homotopy perturbation method by using Chebyshev polynomials. (English)
[J] Arab J. Math. Sci. 18, No. 1, 61-71 (2012). ISSN 1319-5166

Summary: An efficient modification of the homotopy perturbation method is presented by using Chebyshev polynomials. Special attention is given to prove the convergence of the method. Some examples are given to verify the convergence hypothesis, and illustrate the efficiency and simplicity of the method. We compare our numerical results against the conventional numerical method, fourth-order Runge-Kutta method (RK4). From the numerical results obtained from these two methods we find that the proposed technique and RK4 are in excellent conformance. From the presented examples, we find that the proposed method can be applied to a wide class of linear and non-linear ordinary differential equations.

MSC 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
65L06 Multistep, Runge-Kutta, and extrapolation methods
65L20 Stability of numerical methods for ODE

Keywords: homotopy perturbation method; Chebyshev polynomials; convergence; fourth-order Runge-Kutta method; numerical examples

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