# Anyone can describe how euler's method works?

• ddcamp
In summary, the conversation discusses the concept of Euler's method, which is a method used to estimate the next point in a curve given the starting point and slope equation. This method is graphically represented by drawing lines with a slope equal to the step size until reaching the desired point, and then repeating the process.
ddcamp
let's say we do not know the proof.
then how do you guys describe it conceptually?
hm...><

http://en.wikipedia.org/wiki/Euler_method"

Last edited by a moderator:
It's a method to extrapolate the next point in a curve if you only have the starting point and the equation for its slope, since Euler's method is 1st order. Graphically, you're starting at a point and drawing the slope of a line until the horizontal component of the line equals your step size. Then you mark the end point and then based on that point, you calculate the slope of the line at that point and then draw another line. From there, it's lather-rinse-repeat.

## 1. What is Euler's Method?

Euler's Method is a numerical method used to approximate the solutions to ordinary differential equations. It is named after the mathematician Leonhard Euler, who first described the method in the 18th century.

## 2. How does Euler's Method work?

Euler's Method works by approximating a solution to an ordinary differential equation using small, finite steps. It starts with an initial value and then uses the derivative of the function at that point to predict the next point. This process is repeated until the desired endpoint is reached.

## 3. What are the benefits of using Euler's Method?

Euler's Method is a simple and straightforward way to approximate the solutions to ordinary differential equations. It is also computationally efficient and can be easily programmed on a computer.

## 4. Are there any limitations to Euler's Method?

Yes, Euler's Method has some limitations. One of the main limitations is that it can only approximate solutions to first-order ordinary differential equations. It also tends to accumulate errors over time, especially when the step size is large.

## 5. How accurate is Euler's Method?

The accuracy of Euler's Method depends on the step size used. The smaller the step size, the more accurate the approximation will be. However, as mentioned earlier, the method can accumulate errors over time, so it is important to choose an appropriate step size based on the level of accuracy required.

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