Further Acceleration of the Simpson method for solving nonlinear equations

  • Rajinder Thukral Padé Research Centre, England
Keywords: Simpson method, Newton method, Simple root, Nonlinear equation, Root-finding, Order of convergence.

Abstract

There are two aims of this paper, firstly, we present an improvement of the classical Simpson third-order method for finding zeros a nonlinear equation and secondly, we introduce a new formula for approximating second-order derivative. The new Simpson-type method is shown to converge of the order four.  Per iteration the new method requires same amount of evaluations of the function and therefore the new method has an efficiency index better than the classical Simpson method.  We examine the effectiveness of the new fourth-order Simpson-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons is made with classical Simpson method to show the performance of the presented method.

Author Biography

Rajinder Thukral, Padé Research Centre, England

Padé Research Centre, 39 Deanswood Hill, Leeds, West Yorkshire, LS17 5JS, England

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Published
2018-05-25