3 papers
math.DS2021
The SIR model of an epidemic
William G. Faris
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential e…
math-ph2021
Sliding vectors, line bivectors, and torque
William G. Faris
This paper is a modern exposition of old ideas. The setting is a Euclidian space of dimension with associated vector space of dimension . A (non-zero) sliding vector…
math.CO2021
Rooted tree graphs and the Butcher group: Combinatorics of elementary perturbation theory
William G. Faris
The perturbation expansion of the solution of a fixed point equation or of an ordinary differential equation may be expressed as a power series in the perturbation parameter. The t…