A Study on Interval Solutions of Nonlinear Systems

Abstract

Suppose we seek a solution of the nonlinear system f(x={f;(x1,x2, ..., Xn)} = 0 i = 1,2, ..., n where f1, f2, f3, ..., fn are continuous functions on an open set D in R”. There is good many methods for iterative interval solutions of system (I) for any such methods, R. E. Moore developed a technique for finding a safe starting point from which iterates converge, with a particular iterative method in mind, Krawczyk’s operator. Minoru Urabe established an existence and uniqueness theorem (1965) which helps verify the existence and uniqueness of an exact solution and to know the error bound to an approximate solution of a system like (1). His theorem assumes that all the computations are to be carried out in real numbers exactly. Our attempts will be made to combine M. Urabe's theorem and R. E Moore's technique theoretically as well as numerically considering interval version of New­ton's method.