RETRACTED: New numerical method for ordinary differential equations: Newton polynomial

Abstract

This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/our-business/policies/article-withdrawal). This article has been retracted: please see Elsevier Policy on Article Withdrawal (http://www.elsevier.com/locate/withdrawalpolicy). This article has been retracted at the request of the Principal Editors: In the paper, the authors claim that the Adams-Bashforth methods are based on Lagrange interpolation polynomials and that Lagrange polynomials are less accurate than Newton polynomials. The authors state they have devised a new method which is built on Newton interpolation in order to provide better accuracy. After reviewing concerns that were raised by the community, the Principal Editors invited further independent experts to review the claims made by the authors. They find that changing the basis of the polynomial space (Lagrange, Newton, or others) does not change the interpolant polynomial, which is unique when the number of data fits the polynomial degree. Therefore, devising a method based on Newton polynomials, instead of Lagrange polynomials, does not affect the accuracy of the method, but leads to the same method. As such, the Principal Editors have concluded that the findings of the paper are unreliable. This retraction is not related to a breach of ethics. The authors do not agree to this retraction. Apologies are offered to readers of the journal that this was not detected during the submission process.