Mathjs and the Brusselator

As a graduate student I implemented kc to simulate oscillating chemical reactions, and in collaboration with Keld Nielsen, I implemented numerical methods to solve ordinary differential equations (ODEs).

The Brusselator is a fine example of an oscillating chemical reaction, and for most values of the parameters the behavior is pretty fine (meaning that you don’t see very advanced numerical methods to solve it).

I recently noticed that functionality to solve ODEs has been added to Mathjs. To me that is a major development, and it make Mathjs an interesting library to work with. In order to try out the new functionality, I have simulated the Brusselator in JavaScript (using node.js). My little script brussel.js is:

const math = require("mathjs");

const A = 1;
const B = 3;

function brussel(t, c) {
  X = c[0];
  Y = c[1];

  dX = A + X*X*Y - B*X - X;
  dY = B*X - X*X*Y;
  return [dX, dY];
}

let sol = math.solveODE(brussel, [0, 30], [1.0, 1.0], { method: "RK23" });

let n = sol.t.length;
for(let i = 0; i < n; i++) {
  console.log(`${sol.t[i]}, ${sol.y[i][0]}, ${sol.y[i][1]}`);
}

The script outputs a CSV file to stdout, and I run the script as node brussel.js > out. To plot the data, I am using GNUplot. My GNUplot script is very simple:

set terminal 'png'
set output 'brussel.png'

set title 'Brusselator'
plot 'out' using 1:2 title 'X' with lines, 'out' using 1:3 title 'Y' with lines

I hope that Mathjs will add more advanced ODE solvers in the future - in particular methods which can solve stiff equations since many chemical reactions are stiff.