Confidence intervals for finite difference solutions

Publication Date

2018

Journal Title

Communications in Statistics: Simulation and Computation

Abstract

© 2018, © 2018 Taylor & Francis Group, LLC. Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it is only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential equations. In line with this very recent trend, we show how certain commonly used finite difference schemes for numerical solutions of ordinary and partial differential equations can be considered in a regression setting. Focusing on this regression framework, we apply a simple Bayesian strategy to obtain confidence intervals for the finite difference solutions. We apply this framework on several examples to show how the confidence intervals are related to truncation error and illustrate the utility of the confidence intervals for the examples considered.

Volume Number

47

Issue Number

7

Pages

2102 - 2118

Document Type

Article

Status

Faculty

Facility

School of Medicine

Primary Department

Psychiatry

DOI

10.1080/03610918.2017.1335409

Comments

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