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HIGHER ORDER INTERVAL ITERATIVE METHODS FOR NONLINEAR EQUATIONS
HIGHER ORDER INTERVAL ITERATIVE METHODS FOR NONLINEAR EQUATIONS
Journal of applied mathematics & informatics. 2015. Jan, 33(1_2): 61-76
  • Received : April 10, 2014
  • Published : January 30, 2015
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Singh Sukhjit
Gupta D.K.

Abstract
In this paper, a fifth order extension of Potra's third order iterative method is proposed for solving nonlinear equations. A convergence theorem along with the error bounds is established. The method takes three functions and one derivative evaluations giving its efficiency index equals to 1.495. Some numerical examples are also solved and the results obtained are compared with some other existing fifth order methods. Next, the interval extension of both third and fifth order Potra's method are developed by using the concepts of interval analysis. Convergence analysis of these methods are discussed to establish their third and fifth orders respectively. A number of numerical examples are worked out using INTLAB in order to demonstrate the efficacy of the methods. The results of the proposed methods are compared with the results of the interval Newton method.
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