Figure 3
From: Quantifying uncertainty, variability and likelihood for ordinary differential equation models
Two-step procedure. Illustration of the two-step procedure to compute the final pdf at specific points in space. (I) For given discretization/data points ξ i (T), i = 1,...N, the first step is to solve the original ODE backward in time (dashed arrow). (II) For the thus obtained initial values ξ i (0) and their initial density values u0(ξ i (0)), the method of characteristics is used to compute the pdf along the trajectories forward in time (dotted arrow).