Introducing an efficient modification of the homotopy perturbation method by using Chebyshev polynomials

By Mohamed M. Khader. 2012

48 citations recorded by the source corpus.

Abstract In this article 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 compared our numerical results against the conventional numerical method, fourth-order Runge–Kutta method (RK4). From the numerical results obtained from these two methods we found that the proposed technique and RK4 are in excellent conformance. From the presented examples, we found that the proposed method can be applied to a wide class of linear and non-linear ODEs.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3e1ad576645b4ba5079bad00e06e93d65234e922

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In Modeling and Simulation

1. Mohamed M. Khader
2. Ahmed S. Hendy
3. Mehdi Dehghan
4. Nasser Hassan Sweilam

In Numerical Analysis

1. Mohamed M. Khader
2. Ahmed S. Hendy
3. Nasser Hassan Sweilam
4. Mehdi Dehghan

Citations in the corpus

• Numerical treatment for solving fractional Riccati differential equation (2013, methodology): “Several numerical and approximate methods to solve FDEs have been given such as variational iteration method [6], homotopy perturbation method [9], Adomian decomposition method [10], homotopy analysis method [11] and collocation method [12–15].”