# Euler’s Method for Approximating a Solution to a Differential Equation

#### Posted March 3, 2012

#### by Lensyl Urbano

Based on Euler's Method, this interactive graph illustrates a numerical method for solving differential equations. This approach is at the core of many sophisticated computer models of physical phenomena (like climate and weather).- Starting point: (x,y) = ( , )
- Step size:
- Direction:

- Slope equation: dy/dx = x +
- Show analytical solution:

`, you can integrate to find the equation of the curve:`

**Euler's Method**, and is gives a numerical approximation rather than finding the exact, analytical solution using calculus (integration). So why use an approximation when you can find the exact solution? Because, there are quite a number of problems that are impossible or extremely difficult to solve analytically, things like: the diffusion of pollution in a lake; how changing temperature in the atmosphere gives you weather and climate; the flow of groundwater in aquifers; stresses on structural members of buildings; and the list goes on and on. As with most types of numerical approximations, you get better results if you can reduce the step size between projections of the slope. Try changing the numbers and see. A more detailed version, with solutions, is here: Euler's Method. A good reference: Euler's Method by Paul Dawkins.

**Citing this post**: **Urbano**, L., 2012. Euler's Method for Approximating a Solution to a Differential Equation, Retrieved January 20th, 2017, from *Montessori Muddle*: http://MontessoriMuddle.org/ .**Attribution (Curator's Code )**: Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.