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Newton-homotopy analysis method for nonlinear equations. (English) Zbl 1119.65032
Summary: We present an efficient numerical algorithm for solving nonlinear algebraic equations based on Newton-Raphson method and homotopy analysis method. Also, we compare homotopy analysis method with Adomian’s decomposition method and homotopy perturbation method. Some numerical illustrations are given to show the efficiency of the algorithm.

MSC:
65H05 Numerical computation of solutions to single equations
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
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