Abstract
This paper describes a detailed error analysis of the prompt-jump approximation (PJA) and improvements brought upon the accuracy of the PJA by application of the singular perturbation method. The correction factor derived for interpreting the validity of the PJA is effective in estimating numerical errors based on the PJA and calculating its first-order correction. Taking three representative cases (step, ramp and periodic inputs), we examine the numerical errors qualitatively and quantitatively through comparisons with exact solutions obtained by the Runge-Kutta-Merson method. As a result, it is confirmed that solutions based on the PJA would generally result in overestimation in the case of step and ramp inputs, and that the accuracy of the PJA is considerably improved by correction, as evidenced by the numerical examples given in this work.
