The modified exponential time differencing (ETD) method for solving the reactor point kinetics equations

• The modified ETD method is developed to estimate the power transients accurately with large time-step.
• In this method numerical solution converges fast.
• This method is capable of estimating the power transients accurately for longer duration of time.
• It is a self starting method.

The exponential time differencing (ETD) method with Taylor’s series approximation is developed to solve the reactor point kinetics equations using large time-step. It is a semi-analytical and self-starting method in which the point kinetics equations are integrated using an integrating factor. The power and precursor concentrations occurring in the equations are expanded as a polynomial in derivatives. The coefficients of the polynomial are obtained from the recurrence relation. This method is applied to estimate the power transients of both thermal and fast reactors with multi group of delayed neutrons and the results are compared with other standard methods. From the results it is found that the modified exponential time differencing method estimates the power transients accurately for thermal and fast reactors and the numerical solution is found to converge fast. The error analysis of this method is discussed and a criterion for choosing the time-step for step and slowly varying reactivity insertions is also presented.