A Six-Order Method for Non-linear Equations to Find Roots
| Author(s) | : | Manoj Kumar Singh, Arvind K. Singh |
| Institution | : | Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India |
| Published In | : | Vol. 4, Issue 9 — September 2017 |
| Page No. | : | 587-591 |
| Domain | : | Engineering |
| Type | : | Research Paper |
| ISSN (Online) | : | 2348-4470 |
| ISSN (Print) | : | 2348-6406 |
In this paper, new variant of Newton's method based on harmonic mean has been discussed and its sixth orderconvergence has been established. The method generates a sequence converging to the root with a suitable choice ofinitial approximation ????0. In terms of computational cost, it requires evaluations of only two functions and two first orderderivatives per iteration and the efficiency index of the proposed method is 1.5651. Proposed method has been comparedwith some existing methods. Proposed method is free from the evaluation of the second order derivative of the givenfunction as required in the family of Chebyshev–Halley type methods. The efficiency of the method is verified on anumber of numerical examples.
Manoj Kumar Singh, Arvind K. Singh, “A Six-Order Method for Non-linear Equations to Find Roots”, International Journal of Advance Engineering and Research Development (IJAERD), Vol. 4, Issue 9, pp. 587-591, September 2017.
