A simply constructed third-order modifications of Newton's method
Journal of Computational and Applied Mathematics
A cubically convergent Newton-type method under weak conditions
Journal of Computational and Applied Mathematics
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Journal of Computational and Applied Mathematics
Adomian's decomposition method and homotopy perturbation method in solving nonlinear equations
Journal of Computational and Applied Mathematics
ICICS'09 Proceedings of the 7th international conference on Information, communications and signal processing
ISNN'11 Proceedings of the 8th international conference on Advances in neural networks - Volume Part I
Discrete-time ZD, GD and NI for solving nonlinear time-varying equations
Numerical Algorithms
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In this paper, we present a simple, and yet powerful and easily applicable scheme in constructing the Newton-like iteration formulae for the computation of the solutions of nonlinear equations. The new scheme is based on the homotopy analysis method applied to equations in general form equivalent to the nonlinear equations. It provides a tool to develop new Newton-like iteration methods or to improve the existing iteration methods which contains the well-known Newton iteration formula in logic; those all improve the Newton method. The orders of convergence and corresponding error equations of the obtained iteration formulae are derived analytically or with the help of Maple. Some numerical tests are given to support the theory developed in this paper.