A fourth-order method from quadrature formulae to solve systems of nonlinear equations. (English) Zbl 1118.65045

Summary: We obtain a fourth-order convergence method to solve systems of nonlinear equations. This method is based on a quadrature formulae. A general error analysis providing the fourth order of convergence is given. Numerical examples show the fourth-order convergence. This method does not use the second-order Fréchet derivative.


65H10 Numerical computation of solutions to systems of equations
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[1] Ortega, J.M.; Rheinboldt, W.C., Iterative solution of nonlinear equations in several variables, (1970), Academic Press · Zbl 0241.65046
[2] M.T. Darvishi, A. Barati, A third-order Newton-type method to solve systems of nonlinear equations, Appl. Math. Comput., doi:10.1016/j.amc.2006.08.080. · Zbl 1116.65060
[3] Frontini, M.; Sormani, E., Third-order methods from quadrature formulae for solving systems of nonlinear equations, Appl. math. comput., 149, 771-782, (2004) · Zbl 1050.65055
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