How to calculate sensitivity and time constant of differential equation?
Answers
Answer:
Step-by-step explanation:
Given a system of time dependent ordinary differential equations, , where ck are rate parameters, we simultaneously solve for both yi and a set of sensitivity functions, , over all times t. These partial derivatives measure the sensitivity of the solution with respect to changes in the parameters ck. Often these parameters are not accurately known. An example is given from atmospheric chemical kinetics using constant as well as time varying (diurnal) rate parameters. For the purposes of this paper, our calculations considered both first- and second-order contributions to Δy with respect to Δc. It is found that second-order sensitivity terms can be highly significant, but tend to be too costly for present widespread application.