Step size

Definition

Step size is the interval between successive points used in numerical methods for solving differential equations. It determines the accuracy and computational cost of the solution.

5 Must Know Facts For Your Next Test

1. Step size, often denoted as $h$, is a crucial parameter in Euler's method and other numerical techniques.
2. A smaller step size generally increases the accuracy of the numerical solution but also requires more computations.
3. Choosing an appropriate step size involves a trade-off between computational efficiency and accuracy.
4. In adaptive step-size methods, the step size can change dynamically based on error estimates.
5. Large step sizes can lead to significant errors or instability in the numerical solution.

Review Questions

Related terms

Euler's Method:

A simple numerical technique for solving ordinary differential equations using a fixed step size.

Runge-Kutta Methods: A family of iterative methods that provide greater accuracy than Euler’s method by using intermediate points within each step.

Numerical Stability: The property of an algorithm to control errors and produce reliable results, particularly when using larger step sizes.