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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국전산응용수학회 Journal of applied mathematics & informatics Journal of applied mathematics & informatics 제33권 제1호
- 발행연도
- 2015.1
- 수록면
- 61 - 76 (16page)
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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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참고문헌 (22)
참고문헌 신청
A. Cordero. / 2011 / A class of Steffensen type of methods with optimal order of convergence / Appl. Math. Comput 217:7653~7659
A. M. Ostrowski / 1977 / Solution of Equations in Euclidean and Banach spaces 3rd edn / Academic Press
C. Chun. / 2012 / A new sixth-order scheme for nonlinear equations / Appl. Math. Lett 25:185~189
C. Chun. / 2010 / Several new third-order iterative methods for solving nonlinear equations / Acta Appl. Math 109:1053~1063
E. Hansen / 1978 / A globally convergent interval method for computing and bounding real roots / BIT Num. Math 18:415~424
A. M. Ostrowski / 1977 / Solution of Equations in Euclidean and Banach spaces 3rd edn / Academic Press
C. Chun. / 2012 / A new sixth-order scheme for nonlinear equations / Appl. Math. Lett 25:185~189
C. Chun. / 2010 / Several new third-order iterative methods for solving nonlinear equations / Acta Appl. Math 109:1053~1063
E. Hansen / 1978 / A globally convergent interval method for computing and bounding real roots / BIT Num. Math 18:415~424
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