Parameter range reduction for ODE models using monotonic discretizations

This paper analyzes the effectiveness of various monotonic discretizations of an ODE in a parameter range reduction algorithm. Several properties of discretizations are given, and five classes of discretizations are defined for various step numbers ss. The range reduction algorithm that employs these discretizations is described. Using both analytical results based on the prototypical model x′=λxx′=λx, and empirical results based on two more complicated models, it is shown that one particular class of discretizations (the A1OUT class) results in the tightest bounds on the parameters. This result is shown to be attributed to a certain characteristic value, A0A0, of the discretization. Accumulation of these discretizations is also defined, and its usefulness in the range reduction algorithm is described.