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Super cubic iterative methods to solve systems of nonlinear equations. (English) Zbl 1119.65045
Summary: Two super cubic convergence methods to solve systems of nonlinear equations are presented. The first method is based on the Adomian decomposition method. We state and prove a theorem which shows the cubic convergence for this method. But numerical examples show super cubic convergence. The second method is based on a quadrature formula to obtain the inverse of the Jacobian matrix. Numerical examples show high order convergence for both methods.
MSC:
65H10Systems of nonlinear equations (numerical methods)