Representation of simulation errors in single step methods using state dependent noise

The local error of single step methods is modelled as a function of the state derivative multiplied by bias and zero-mean white noise terms. The deterministic Taylor series expansion of the local error depends on the state derivative meaning that the local error magnitude is zero in steady state and...

Full description

Saved in:
Bibliographic Details
Published in:MATEC web of conferences 2021, Vol.347, p.1
Main Author: Boje, Edward
Format: Article
Language:English
Subjects:
Algorithms
Computer simulation
Derivatives
Differential equations
Noise
Series expansion
Simulation
State estimation
State vectors
Stochastic models
Taylor series
White noise
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The local error of single step methods is modelled as a function of the state derivative multiplied by bias and zero-mean white noise terms. The deterministic Taylor series expansion of the local error depends on the state derivative meaning that the local error magnitude is zero in steady state and grows with the rate of change of the state vector. The stochastic model of the local error may include a constant, “catch-all” noise term. A continuous time extension of the local error model is developed and this allows the original continuous time state differential equation to be represented by a combination of the simulation method and a stochastic term. This continuous time stochastic differential equation model can be used to study the propagation of the simulation error in Monte Carlo experiments, for step size control, or for propagating the mean and variance. This simulation error model can be embedded into continuous-discrete state estimation algorithms. Two illustrative examples are included to highlight the application of the approach.
ISSN:2261-236X
2274-7214
2261-236X
DOI:10.1051/matecconf/202134700001