Differential Equations › Section B · First order differential equations › Topic B.10
Runge-Kutta and multistep methods
Euler's method uses one slope per step and pays for it with slow convergence. Sampling the slope more cleverly, or reusing slopes already computed, gives methods that are far more accurate for the same work, and these are the methods real software uses.
In this topic
- Better slopes, not just smaller steps
- Heun's method
- The classical Runge-Kutta method
- Worked example: one step of each
- Worked example: equal work
- Checking the order
- Adaptive step sizes
- Multistep methods
- Stiff problems and long simulations
- Common mistakes to avoid
- Key takeaways
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