AppliedMath, Vol. 5, Pages 138: A Two-Stage Numerical Algorithm for the Simultaneous Extraction of All Zeros of Meromorphic Functions

AppliedMath doi: 10.3390/appliedmath5040138

Authors:
Ivan K. Ivanov
Stoil I. Ivanov

In this paper, we present an effective two-stage numerical algorithm for the simultaneous finding of all roots of meromorphic functions in a region within the complex plane. At the first stage, we construct a polynomial with the same roots as the ones of the considered function; at the next step, we apply some method for the simultaneous approximation of its roots. To show the efficiency and applicability of our algorithm together with its advantages over the classical Newton, Halley and Chebyshev’s iterative methods, we conduct three numerical examples, where we apply it to two test functions and to an important engineering problem.

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Ivan K. Ivanov www.mdpi.com