Title
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
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