A Taylor series solution of the reactor point kinetics equations

TL;DR

This paper presents a simple, transparent, and highly accurate numerical method based on Taylor series expansion for solving reactor point kinetics equations, demonstrating comparable results to more complex methods.

Contribution

It introduces a first-order Taylor series expansion approach for reactor kinetics, offering a straightforward and accurate alternative to existing methods.

Findings

Results are comparable to other methods across various reactivity inputs.

The algorithm is simple, transparent, and highly accurate.

Effective for different initial conditions and reactivity types.

Abstract

The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step gives results that are comparable to those obtained using other popular and more complicated methods. The algorithm developed using a Taylor series expansion is simple, completely transparent, and highly accurate. The procedure is tested using a variety of initial conditions and input data, including step reactivity, ramp reactivity, sinusoidal, and zigzag reactivity. These results are compared to those obtained using other methods.