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Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations. (English) Zbl 1204.65050
The authors consider two third order Chebyshev-like methods for solving systems of nonlinear equations. It is proved that the methods can be obtained by approximating the second derivatives in the Chebyshev methods. In addition, the authors show the local and cubic convergence of both methods using point attraction theory. Finally, they also compare the computational cost of the two methods with the classical Newton method, and they apply the methods to solve some systems of nonlinear equations including an application to the Chandrasekhar integral equations.

MSC:
65H10 Numerical computation of solutions to systems of equations
65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
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