Modelling the discretization error of initial value problems using the Wishart distribution

Naoki Marumo; Takeru Matsuda; Yuto Miyatake

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arXiv · 2306.04084

Modelling the discretization error of initial value problems using the Wishart distribution

Naoki Marumo·Takeru Matsuda·Yuto Miyatake

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Abstract

This paper presents a new discretization error quantification method for the numerical integration of ordinary differential equations. The error is modelled by using the Wishart distribution, which enables us to capture the correlation between variables. Error quantification is achieved by solving an optimization problem under the order constraints for the covariance matrices. An algorithm for the optimization problem is also established in a slightly broader context.

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Naoki Marumo, Takeru Matsuda, Yuto Miyatake. 2023-06-07. Modelling the discretization error of initial value problems using the Wishart distribution. https://arxiv.org/abs/2306.04084

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