Pseudocomposition: a technique to design predictor-corrector methods for systems of nonlinear equations

A new technique for designing iterative methods for solving nonlinear systems is presented. This procedure, called pseudocomposition, uses a known method as a predictor and the Gaussian quadrature as a corrector. The order of convergence of the resulting scheme depends, among other factors, on the order of the last two steps of the predictor. We also introduce a new iterative algorithm of order six, and apply the mentioned technique to generate a new method of order ten. Finally, some numerical test are shown. 2012 Elsevier Inc. All rights reserved.This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion, Universitat Politecnica de Valencia PAID-06-2010-2285.Cordero Barbero, A.; Torregrosa Sánchez, JR.; Vassileva, MP. (2012). Pseudocomposition: a technique to design predictor-corrector methods for systems of nonlinear equations. Applied Mathematics and Computation. 218(23):11496-11504. https://doi.org/10.1016/j.amc.2012.04.08111496115042182