Solution of nonlinear equations using three point Gaussian quadrature formula and decomposition technique

Abstract

The problem of solving nonlinear equations (real or complex) is a nontrivial task in many areas of science and engineering. Usually, the analytic methods for such equations are not directly affordable and require an iterative approach for getting an approximate solution. Keeping in view the above facts, we suggest and analyze some new iterative methods for solving nonlinear equation of the form f(u) = 0 by using the decomposition technique coupled with a system of equations and threepoints Gaussian quadrature formula. We also determine the convergence order of our proposed iterative methods. Some test examples are given to endorse and validate the performance of new methods as compared to previously well-known methods.