## An application of graph theory in numerical analysis

- Feb. 3, 2017
- 2:30 p.m.
- LeConte 312

## Abstract

John C. Butcher has developed methods for analyzing the order of Runge-Kutta methods with the aid of rooted trees. He used trees as a substitute for summands in a derivative of a function and replaced the product rule and the chain rule with certain operations on trees. He has also proven a Taylor theorem with summation over all rooted trees and a criterion for a Runge-Kutta method to have order p, for any natural p.