Euler's Method
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May 1, 2024
4 minute read
Euler's Method is a numerical method for approximating the solution to a differential equation. It is a first-order method, which means that it uses the value of the solution at the previous point in time to approximate the value at the current point in time.
What is Euler's Method?
Euler's Method is based on the idea of using a linear approximation to the solution of a differential equation. The linear approximation is given by the following equation:
$$y_{i+1} = y_i + h \cdot f(x_i, y_i)$$
where:
- $y_{i+1}$ is the approximate value of the solution at the point $x_{i+1}$
- $y_i$ is the approximate value of the solution at the point $x_i$
- $h$ is the step size
- $f(x_i, y_i)$ is the value of the differential equation at the point $(x_i, y_i)$
Why is Euler's Method important?
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Find a path to becoming a Euler's Method. Learn more at:
OpenCourser.com/topic/ocjryr/euler
