Statistical analysis of differential equations: introducing probability measures on numerical solutions.

ABSTRACT: In this paper, we present a formal quantification of uncertainty induced by numerical solutions of ordinary and partial differential equation models. Numerical solutions of differential equations contain inherent uncertainties due to the finite-dimensional approximation of an unknown and implicitly defined function. When statistically analysing models based on differential equations describing physical, or other naturally occurring, phenomena, it can be important to explicitly account for the uncertainty introduced by the numerical method. Doing so enables objective determination of this source of uncertainty, relative to other uncertainties, such as those caused by data contaminated with noise or model error induced by missing physical or inadequate descriptors. As ever larger scale mathe

SUBMITTER: Conrad PR 

PROVIDER: S-EPMC7089645 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature