Numerical solution of the integro-differential equation of the point kinetics of nuclear reactors as an ODE

• The integro-differential equation (IDE) of the point kinetics was solved as an ODE.
• The ODE independent term was obtained with Lagrange interpolation polynomial (LIP).
• A 2nd degree LIP algorithm (IQL2) showed better accuracy than the results of 2009.
• For 3-to-4-digit accuracy, and Δt⩽10-3s, IQL2 is as accurate as other highly accurate codes.
• It is simple and efficient, it is however sensitive to the number of computing digits used.

The integro-differential equation (IDE) of the reactor point kinetics was numerically solved as an ODE. The integral term of the IDE was taken as an independent term of the ODE and it was calculated with an estimate of the neutron density (ND) using the Lagrange interpolation polynomials, then the exact solution of the resultant ODE (IQLn algorithms) is obtained. Four applications were used to assess the accuracy of the algorithms: a mild ramp, a fast ramp, a sinusoidal and a feedback type of reactivity insertion. The 2nd degree polynomial algorithm (IQL2) showed that for about 3-to-4-digit accuracy and Δt⩽10-3Δt⩽10-3, it was as accurate as other highly accurate codes, and that it is very efficient.