Variational Iteration Technique and Numerical Methods for Solving Nonlinear Equations

Abstract

Various problems of pure and applied sciences such as physics, chemistry, biology, engineering, economics, management sciences, industrial research and optimization can be studied in the unified frame work nonlinear equation f ( x) = 0. In this thesis, we use the variational iteration technique and its various modifications to suggest and analyze several iterative methods for finding the approximate solution of the nonlinear equations. Using suitable finite difference schemes, a number of new iterative methods free from second derivative are considered and analyzed. Variational iteration technique is also used to find the multiple roots of nonlinear equations with known and unknown multiplicity. Several examples are given to illustrate the efficiency and implementation of these new methods. Comparison with other methods is given to show the performance of new methods.