# zbMATH — the first resource for mathematics

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:
 65H10 Numerical computation of solutions to systems of equations
Full Text:
##### References:
  Adomian, G., Solving frontier problem of physics: the decomposition method, (1994), Kluwer Academic Publishers Dordrecht · Zbl 0802.65122  Babolian, E.; Biazar, J., On the order of convergence of Adomian method, Appl. math. comput., 130, 383-387, (2002) · Zbl 1044.65043  Chun, Ch., A new iterative method for solving nonlinear equations, Appl. math. comput., 178, 2, 415-422, (2006) · Zbl 1105.65057  Chen, W.; Lu, Z., An algorithm for Adomian decomposition method, Appl. math. comput., 159, 135-221, (2004) · Zbl 1062.65059  Cherruault, Y., Convergence of adomisn’s method, Kybernetes, 9, 2, 31-38, (1988)  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  Ortega, J.M.; Rheinboldt, W.C., Iterative solution of nonlinear equations in several variables, (1970), Academic Press · Zbl 0241.65046  Wazwaz, A.M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. math. comput., 111, 53-69, (2000) · Zbl 1023.65108
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.