Estimating the error term in the Trapezium Rule using a Runge-Kutta method
Numerical Analysis
2023-06-13 v1 Numerical Analysis
Abstract
We show how the error term for the Trapezium Rule can be estimated, by solving an initial value problem using a Runge-Kutta method. The error term can then be added to the Trapezium approximation, yielding a much more accurate result. We also show how the risk of singularities in the relevant initial value problem can be mitigated.
Cite
@article{arxiv.2306.06785,
title = {Estimating the error term in the Trapezium Rule using a Runge-Kutta method},
author = {J. S. C. Prentice},
journal= {arXiv preprint arXiv:2306.06785},
year = {2023}
}