Mr. Integral

THE BIG IDEA

Numerical Methods

How do we trust a numerical trajectory?

A numerical method advances an approximate state using sampled slopes. Improve the local estimate, then check global error and stability separately: a small-looking step can still be unsuitable for a stiff equation.

Begin the first lesson →See the lesson route ↓

3 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Euler steps
  2. better local estimates give02Higher-order slopes
  3. trusting the trajectory requires03Stability & error

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit3 lessons
  1. 01Euler’s Method and Local SlopesApproximate an initial-value problem and compare numerical steps with an exact solution.
  2. 02Midpoint, Heun and Runge–Kutta MethodsImprove slope estimates and understand what the advertised order assumes.
  3. 03Numerical Stability, Error and StiffnessDistinguish accuracy from stable propagation and identify a stiffness restriction.