On new iterative method for solving systems of nonlinear equations. (English) Zbl 1197.65048

Author’s abstract: Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have been proposed. In this paper, we employ the Homotopy Analysis Method (HAM) to derive a family of iterative methods for solving systems of nonlinear algebraic equations. Our approach yields second and third order iterative methods which are more efficient than their classical counterparts such as Newton’s, Chebychev’s and Halley’s methods.


65H10 Numerical computation of solutions to systems of equations
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
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