I'm a professor of mathematics at the University of North Carolina Asheville. I've also done a fair amount of consulting work over the years focusing on scientific and data visualization.
I'm happy to be part of the first Observable Ambassador's cohort.
Public
Edited
Nov 17, 2022
Importers
9 stars
orbit = rk4(([x, y], t) => [-y - x / t, x - y / 2], [1, 1], 1, 0.5, 100, 1000)
{
let w = 0.8 * width;
let h = 0.6 * w;
let plot = plotter({
xDomain: [-1, 3],
yDomain: [1.5, -0.5],
width: w,
height: h
});
plot.polyline(orbit.map(([x, y]) => ({ x: x, y: y })));
return plot.node;
}
// Run RK4 forwards and backwards over the time interval [a,b] where t0 is in [a,b], like
// rk4(([x]) => [x], [1], 0, -5, 5, 100)
function rk4(f, y0, t0, a, b, n) {
let dt = (b - a) / n;
if (t0 == a) {
// Just go forward
return rk4_multi_step(f, y0, a, dt, n);
} else if (b == t0) {
// Just go backward
let result = rk4_multi_step(f, y0, b, -dt, n);
result.reverse();
return result;
} else if (a < t0 && t0 < b) {
// Go forward and backward and concatenate
let i = Math.floor((t0 - a) / dt);
let backward = rk4_multi_step(f, y0, t0, -dt, i);
backward.reverse();
let forward = rk4_multi_step(f, y0, t0, dt, n - i).slice(1);
return backward.concat(forward);
}
}
// Take a bunch of RK4 steps, like
// rk4_multi_step(([x]) => [x], [1], 0, 0.1, 10)
function rk4_multi_step(f, y0, t0, dt, n) {
let y = y0;
y.t = t0;
let ys = [y];
for (let i = 0; i < n; i++) {
y = rk4_single_step(f, y, t0 + i * dt, dt);
y.t = t0 + (i + 1) * dt;
// Implement an overly simple bailout
// ys.push(y);
if (d3.sum(y.map((x) => x ** 2)) < 10 ** 8 && y.filter(isNaN).length == 0) {
ys.push(y);
} else {
return ys;
}
}
return ys;
}
// Take a single RK4 step from t0 to t0+dt, like
// rk4_single_step(([x]) => [x], [1], 0, 0.1)
function rk4_single_step(f, y0, t0, dt) {
let dt2 = dt / 2;
let k1 = f(y0, t0);
let k2 = f(add(y0, mul(dt2, k1)), t0 + dt2);
let k3 = f(add(y0, mul(dt2, k2)), t0 + dt2);
let k4 = f(add(y0, mul(dt, k3)), t0 + dt);
let s1 = add(k1, mul(2, k2));
let s2 = add(s1, mul(2, k3));
let s3 = add(s2, k4);
return add(y0, mul(dt / 6, s3));
}
// Multiply a vector by a scalar, like
// mul(2,[3,4])
function mul(r, a) {
return a.map(x => r * x);
}
// add two vectors, like
// add([1, 2], [3, 4])
function add(a1, a2) {
return a1.map((a, i) => a + a2[i]);
}
d3 = require('d3-array@2')
// Fork of '@kjerandp/plotter'
import { plotter } from '50dadfdec01c15a8'
n = 4
init = d3.range(0, 1 + 1 / n, 1 / n).map(x => 4 * (x - x ** 2))
d3.range(0, 1 + 1 / n, 1 / n)
function F(u, t) {
let v = Array.from({ length: n });
v[0] = 0;
v[n] = 0;
for (let i = 1; i < n; i++) {
v[i] = n ** 2 * (u[i + 1] - 2 * u[i] + u[i - 1]);
}
return v;
}
// rk4_multi_step(f, y0, t0, dt, n)
// rk4(f, y0, t0, a, b, n)
// orbit = rk4(([x, y], t) => [-y - x / t, x - y / 2], [1, 1], 1, 0.5, 100, 1000)
result = rk4(F, init, 0, 0, 1, 10)
import { odeRK4 } from '@rreusser/integration'
odeRK4
init
yy = d3.range(n + 1)
yy
init
rresult = {
let y = d3.range(0, 1 + 1 / n, 1 / n).map(x => 4 * (x - x ** 2));
for (let i = 0; i < 1000; i++) {
odeRK4(y, y, f, 0.001);
}
return y;
}
function f(_, u) {
let v = Array.from({ length: n });
v[0] = 0;
v[n] = 0;
for (let i = 1; i < n; i++) {
v[i] = n ** 2 * (u[i + 1] - 2 * u[i] + u[i - 1]);
}
return v;
}
Purpose-built for displays of data
Observable is your go-to platform for exploring data and creating expressive data visualizations. Use reactive JavaScript notebooks for prototyping and a collaborative canvas for visual data exploration and dashboard creation.
