Further Improvement of Simpson-type Methods for Solving Nonlinear Equations

摘要

The aim of this paper is to present further improvement of the Simpson-type methods for finding zeros of a nonlinear equation. The new Simpson-type methods are shown to converge of the same order four and five, but with better precision of the zeros. In terms of computational cost, the new iterative methods require four evaluations of functions per iteration and therefore the new methods have an efficiency index better than the classical Simpson method. It is proved that the new methods have a convergence of order four and five. We examine the effectiveness of the new Simpson-type methods by approximating the simple root of a given nonlinear equation. Numerical comparisons are included to demonstrate exceptional convergence speed of the proposed methods and thus verifies the theoretical results.