Higher order multi-step interval iterative methods for solving nonlinear equations in $$R^n$$ R n

Abstract

In this paper, higher order multi-step interval iterative methods are proposed for solving nonlinear equations in \(R^n\). Each method leads to an an interval vector enclosing the approximate solution along with the rigorous error bounds automatically. These methods require solving linear interval systems of equations. Interval extension of Gaussian elimination algorithm is described and used for solving them. The convergence analysis of both the methods is established to show their third and fourth order of convergence. A number of numerical examples are worked out and the performance in terms of iterations count and diameters of resulting interval vectors are measured.