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Introducing an efficient modification of the homotopy perturbation method by using Chebyshev polynomials. (English) Zbl 1236.65079
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:
65L05 Numerical methods for initial value problems
34A34 Nonlinear ordinary differential equations and systems, general theory
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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