Solutions of Nonlinear Problems: NEWTON-TYPE ITERATIVE METHODS FOR SYSTEMS OF NONLINEAR PROBLEMS

The principal objective of this book is to construct iterative methods for the solution of systems of nonlinear problems arising from diverse fields. This manuscript spells out the formulation of iterative schemes for nonlinear equations, the system of nonlinear equations, nonlinear boundary value problems and nonlinear initial value problems in ordinary differential equations. First, we present a cubically convergent Newton type iterative method to obtain the numerical solution of nonlinear equations. This method is built by using a quadrature rule based on Haar wavelet. Then we propose a pair of Newton type methods to solve the system of nonlinear equations. The theoretical investigation shows that the proposed methods are of third and fifth order convergence respectively. We have also suggested a three-step numerical method with nineth order convergence to solve the system of nonlinear equations stemming out of Bratu-type nonlinear boundary value problems. We present an alternative numerical method to find the numerical solution of initial value problems. A new method is suggested for the numerical solution of nonlinear system of initial value problems.