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math.NA2024
Quantifying uncertainty in the numerical integration of evolution equations based on Bayesian isotonic regression
Yuto Miyatake, Kaoru Irie, Takeru Matsuda
This paper presents a new Bayesian framework for quantifying discretization errors in numerical solutions of ordinary differential equations. By modelling the errors as random vari…
math.NA2024
On the B-series composition theorem
John C. Butcher, Taketomo Mitsui, Yuto Miyatake +1
The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem…