Jacobi Elliptic Functions in the Complex PlaneComputing π with the Bailey-Borwein-Plouffe FormulaAdaptive Contouring in Fragment ShadersGrouping Points with Principal Component AnalysisDomain Coloring with Adaptive ContouringDouble Compound Pendulums3D Reaction-DiffusionQuasicrystals2D (Non-physical) N-body Gravity with Poisson's EquationPeriodic Planar Three-Body OrbitseasesFinding Roots in the Complex Planeglsl-complexglsl-complex-auto-differentiationpolynomial-rootscomplex-auto-differentiationutils
Integration
adaptiveSimpson(Math.sin, 0, Math.PI)
adaptiveSimpson(Math.sin, 0, Math.PI, {
tolerance: 1e-11,
maxDepth: 8,
minDepth: 2
})
adaptiveSimpson(x => 2 ** n * x * Math.sin(2 ** n * x), 0, Math.PI, {
tolerance: 1e-12,
minDepth: n - 1,
maxDepth: 12
})
vectorAdaptiveSimpson(t => [Math.sin(t), Math.cos(t)], 0, Math.PI)
vectorAdaptiveSimpson([], // output destination (optional)
(out, t) => {out[0] = Math.sin(t); out[1] = Math.cos(t)},
0, Math.PI, // a, b
1e-11, // tolerance (optional)
8, // max recursion depth (optional)
2) // dimension (optional, otherwise inferred from f)
{
var y = [1, 0];
var steps = 20;
var dt = (Math.PI * 2) / steps;
var t = 0;
for (var i = 0; i < steps; i++) {
odeRK2(
y,
y,
(yp, y, t) => {
yp[0] = y[1];
yp[1] = -y[0];
},
dt
);
t += dt;
}
return y;
}
{
var y = [1, 0]
var steps = 20
var dt = Math.PI * 2 / steps
for (var i = 0; i < steps; i++) {
odeRK2(y, y, (_, y) => [y[1], -y[0]], dt)
}
return y
}
{
var y = [1, 0]
var steps = 20
var dt = Math.PI * 2 / steps
var t = 0
for (var i = 0; i < steps; i++){
odeRK4(y, y, (yp, y, t) => {
yp[0] = y[1];
yp[1] = -y[0]
}, dt)
t += dt
}
return y
}
{
var y = [1, 0]
var steps = 20
var dt = Math.PI * 2 / steps
for (var i = 0; i < steps; i++) {
odeRK4(y, y, (_, y) => [y[1], -y[0]], dt)
}
return y
}
{
var yn = [[1, 0]]
var steps = 10
var dt = Math.PI * 2 / steps
for (var i = 0; i < steps; i++) {
yn.push(odeRK4([], yn[i], (_, y) => [y[1], -y[0]], dt))
}
return yn
}
{
var state = {y: [1, 0], t: 0}
var options = {tLimit: Math.PI * 2 * 100.0, tolerance: 1e-15}
var t1 = performance.now();
while (!state.limitReached) {
ode45(state, (yp, y, t) => {yp[0] = y[1], yp[1] = -y[0]}, options)
}
var t2 = performance.now();
console.log(t2 - t1)
return state
}
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