New Third-Order Schroder-Type Method for Finding Zeros of Nonlinear Equations Having Unknown Multiplicity

摘要

The aims of this paper are, firstly, to define a new third-order Schroder-type method for finding zeros of nonlinear equations having unknown multiplicity and secondly, to introduce a new formula for approximating the multiplicity of the iterative method. In terms of computational cost the new iterative method requires four evaluations of functions per iteration. It is proved that the new method has a convergence of order three. Numerical comparisons are included to demonstrate exceptional convergence speed of the proposed method.