• Corpus ID: 119733555

Compositionality of the Runge-Kutta Method

@article{Ngotiaoco2017CompositionalityOT,
  title={Compositionality of the Runge-Kutta Method},
  author={Timothy Ngotiaoco},
  journal={arXiv: Category Theory},
  year={2017}
}
  • Timothy Ngotiaoco
  • Published 10 July 2017
  • Computer Science, Mathematics
  • arXiv: Category Theory
In Spivak's work, dynamical systems are described in terms of their inputs and outputs in a pictorial way using an operad of wiring diagrams. Each dynamical system is a box with certain inputs and outputs, and multiple dynamical systems are linked together using wiring diagrams, which describe how the outputs of one dynamical system to the inputs of another. By describing dynamical systems in this way, we can decompose a large dynamical system as a collection of smaller, simpler dynamical… 
Open Petri nets
  • J. BaezJ. Master
  • Computer Science
    Mathematical Structures in Computer Science
  • 2020
TLDR
Two forms of semantics for open Petri nets are described using symmetric monoidal double functors out of pen(Petri), including an operational semantics and a reachability semantics that simply says which markings of the outputs can be reached from a given marking of the inputs.

References

SHOWING 1-3 OF 3 REFERENCES
The steady states of coupled dynamical systems compose according to matrix arithmetic
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way.
Framed bicategories and monoidal fibrations
In some bicategories, the 1-cells are `morphisms' between the 0-cells, such as functors between categories, but in others they are `objects' over the 0-cells, such as bimodules, spans, distributors,
Constructing symmetric monoidal bicategories
We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently