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

• Why does a smaller step size typically result in a more accurate solution?
• How does changing the step size affect computational cost?
• What is an adaptive step-size method?

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.