An optimal multiple root-finding method of order three
Journal of Computational and Applied Mathematics
High-order nonlinear solver for multiple roots
Computers & Mathematics with Applications
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
Journal of Computational and Applied Mathematics
Iterative methods for solving nonlinear equations with finitely many roots in an interval
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
For a nonlinear equation f(x)=0 having a multiple root we consider Steffensen's transformation, T. Using the transformation, say, F"q(x)=T^qf(x) for integer q=2, repeatedly, we develop higher order iterative methods which require neither derivatives of f(x) nor the multiplicity of the root. It is proved that the convergence order of the proposed iterative method is 1+2^q^-^2 for any equation having a multiple root of multiplicity m=2. The efficiency of the new method is shown by the results for some numerical examples.