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Zbl 1192.65053
Noor, Muhammad Aslam
Iterative methods for nonlinear equations using homotopy perturbation technique. (English)
[J] Appl. Math. Inf. Sci. 4, No. 2, 227-235 (2010). ISSN 1935-0090

Summary: We suggest and analyze some iterative methods for solving nonlinear equations using {\it J.-H. He's} homotopy perturbation technique [Appl. Math. Comput. 135, No.~1, 81--84 (2003; Zbl 1023.65039)] coupled with a system of equations. In addition, we show that the homotopy polynomial is exactly the Adomian polynomial and this establishes the equivalence between the homotopy perturbation and the decomposition techniques. Our method of establishing the equivalence between these methods is very simple as compared with others.

MSC 2000:: *65H05 Single nonlinear equations (numerical methods)

Keywords: homotopy perturbation method; iterative method; convergence; Newton method; coupled system of equations; nonlinear equations; Adomian polynomial

Citations: Zbl 1023.65039

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