Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Hobbyists & Makers · Euler vs RK4

Euler vs RK4 for a Fibonacci sequence

Built for hobbyists & makers exploring it for fun. Play with real physics and math, no license and no setup — just open and tinker. Simulate a Fibonacci sequence live below — adjust the inputs and watch it respond, right in your browser.

Numerical Methods — Euler vs RK4Live

ODE integration accuracy

Controls

Solving dy/dt = y (true answer eᵗ). Euler drifts badly at large step sizes; RK4 hugs the exact curve. Shrink the step and both improve — RK4 far faster.

Presets

Step size h

▶ Run in Python

Data Inspector

Step h0.50

Euler error8.695

RK4 error2.07e-2

RK4 order4th

Governing equation

y_{n + 1} = y_{n} + h f (t_{n}, y_{n}), h = 0.50

Reading this result: Halving the step roughly halves Euler's error (1st order) but cuts RK4's by ~16× (4th order): that steep payoff is why RK4 dominates for smooth problems.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Students Researchers Educators Engineers K-12 Students First Responders General version →

More with Euler vs RK4

Euler vs RK4 for compound interest Euler vs RK4 for a population curve Euler vs RK4 for a loan payoff Euler vs RK4 for a logistic map Euler vs RK4 for a fractal tree Euler vs RK4 for a Fourier series Euler vs RK4 for a Taylor approximation Euler vs RK4 for a Monte-Carlo pi estimate

Frequently asked questions

Is this good for hobbyists & makers?: Yes — this version of "Euler vs RK4 for a Fibonacci sequence" is framed for hobbyists & makers exploring it for fun. Play with real physics and math, no license and no setup — just open and tinker.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.