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

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