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.