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High order iterative methods without derivatives for solving nonlinear equations. (English) Zbl 1119.65036

New second-order and third-order iterative methods based on the homotopy perturbation theory are presented for solving nonlinear equations. These methods do not need to compute the derivatives. The second-order iterative method has the same asymptotic error constant and convergence rate compared with the Newton-method. The third-order iterative method has a faster rate of convergence and high precision compared with the Newton method and the new second-order iterative methods.

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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References:

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