Approximating Solutions Using Euler’s Method
Samuel Baker
6 min read
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Study Guide Overview
This study guide covers Euler's Method for approximating function values given a differential equation and initial condition. It explains the method's algorithm, including calculating the change in y using the slope derived from the differential equation and a step size. Examples demonstrate how to approximate y(x) for given values and step sizes. Finally, a practice problem explores calculating absolute error and the impact of step size on approximation accuracy.
#What is Euler's Method?
Euler’s method is a way to find the numerical values of functions based on a given differential equation and an initial condition. We can approximate a function as a set of line segments using Euler’s method. 📈
Before introducing this idea, it is necessary to understand two basic ideas.
This information allows us to do an algorithmic process to approximate function values when given a differential equation and an initial condition.
To showcase this method, let’s consider the following differential equation with a consequent initial condition:
Let’s say we want to approximate y(7). We will create a tab...
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