Browsing 3. Tεχνικές Αναφορές | Technical Reports by Subject "Analytical formulae"
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- ItemOpen AccessA new method for the computation of the zeros of analytic functions
Γενικό Τμήμα (Τεχνικές Αναφορές)Ioakimidis, Nikolaos; Anastasselou, Eleni; Ιωακειμίδης, Νικόλαος; Αναστασέλου, ΕλένηA new method for the computation of the zeros of analytic functions (or the poles of meromorphic functions) inside or outside a closed contour C in the complex plane is proposed. This method is based on the Cauchy integral formula (in generalized forms) and leads to closed-form formulae for the zeros (or the poles) if they are no more than four. In general, for m zeros (or poles) these can be evaluated as the zeros of a polynomial of degree m. In all cases, complex contour integrals have to be evaluated numerically by using appropriate numerical integration rules. Several practical algorithms for the implementation of the method are proposed and the method of Abd-Elall, Delves and Reid is rederived by two different approaches as one of these algorithms. A numerical application to a transcendental equation appearing in the theory of neutron moderation is also made and numerical results of high accuracy are easily obtained.
- ItemOpen AccessA real closed-form integral formula for roots of nonlinear equations
Γενικό Τμήμα (Τεχνικές Αναφορές)Ioakimidis, Nikolaos; Ιωακειμίδης, ΝικόλαοςAn analytical integral formula for a single simple root of a nonlinear equation in a finite interval is proposed. The derivation of this formula is based on Picard's method for the number of roots of nonlinear equations and on Green's theorem. The present formula is particularly useful for the location of roots of nonanalytic functions. A comparison between the present formula and a related classical formula based on the theory of analytic functions is also made.