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Polynomial approach method to solve the neutron point kinetics equations with use of the analytic continuation

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Published/Copyright: December 8, 2016
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Abstract

In this work, we report a solution to solve the Neutron Point Kinetics Equations applying the Polynomial Approach Method. The main idea is to expand the neutron density and delayed neutron precursors as a power series considering the reactivity as an arbitrary function of the time in a relatively short time interval around an ordinary point. In the first interval one applies the initial conditions and the analytical continuation is used to determine the solutions of the next intervals. A genuine error control is developed based on an analogy with the Rest Theorem. For illustration, we also report simulations for different approaches types (linear, quadratic and cubic). The results obtained by numerical simulations for linear approximation are compared with results in the literature.

Kurzfassung

In dieser Arbeit wird über die Lösung punktkinetischer Gleichungen durch Anwendung polynomgestützter Methoden berichtet. Der Hauptgedanke dabei ist die Entwicklung der Neutronendichte und der Vorläufer verzögerter Neutronen als Potenzreihe unter Betrachtung der Reaktivität als eine beliebige Funktion der Zeit in einem relativ kurzen Zeitintervall um einen gewöhnlichen Punkt. Im ersten Intervall werden die Anfangsbedingungen und die analytische Fortsetzung zur Bestimmung der Lösungen des nächsten Intervalls verwendet. Auf der Basis des Rest-Theorems wurde eine Methode zur Fehlervermeidung entwickelt. Zur Veranschaulichung werden Simulationen verschiedener Ansätze (linear, quadratisch und kubisch) beschrieben. Die durch numerische Simulationen erhaltenen Ergebnisse werden mit Ergebnissen aus der Literatur verglichen.

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Received: 2016-09-30
Published Online: 2016-12-08
Published in Print: 2016-12-16

© 2016, Carl Hanser Verlag, München

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