Written by the Fiveable Content Team • Last updated August 2025
Verified for the 2027 exam
Verified for the 2027 exam•Written by the Fiveable Content Team • Last updated August 2025
Definition
A first-order numerical procedure is an algorithm used to approximate solutions to first-order ordinary differential equations. It involves dividing the interval into small steps and using iterative calculations to estimate values at each step.
AP course connection
Topic 7.5: 7.5 Approximating Solutions Using Euler’s Method
Euler's method is a specific first-order numerical procedure that uses linear approximations to estimate solutions.
Runge-Kutta Methods: Runge-Kutta methods are more accurate and sophisticated first-order numerical procedures that use weighted averages of multiple estimates at each step.
Taylor Series Method: The Taylor series method expands the function into an infinite sum of terms, allowing for higher accuracy in approximating solutions.