System of Nonlinear Equation and MATLAB

We extend the idea of Otolorin's for solving a single variable nonlinear equation to a system of non linear equations, Permitting Singular Jacobian at some points in the vicinity of the required root. It is proved that this modification has quadratic convergence. Using this modification, we further presented new cubically convergent Predictor-corrector type method free from second order derivative. The proposed algorithms are simple and straight forward to implement, Several numerical examples are given to illustrate their efficiency and the performance of the presented methods Therefore, this book provide various method of different order of convergence and this book may be viewed as an extension and generalization of the existing methods.