A modified piecewise constant approximation for solution to the point kinetics equations

A new enabling form of the PCA algorithm for high accuracy solutions to the PKEs, called Modified PCA (MPCA), has been presented and demonstrated to solve PKEs with time- dependent prescribed and non-linear reactivity insertions. The new form relegates the reactivity to a source term by introducing an ad-hoc constant prompt step reactivity. Remarkably, in so doing. the numerical difficulty associated with time-dependent and non-linear reactivity greatly diminishes. The MPCA gives all literature benchmarks known to the author to 9 or more significant places. This method therefore becomes one of a trifecta of existing methods to reliably generate high fidelity benchmarks for the PKEs for both prescribed and non-linear reactivity insertions.