Anyone can describe how euler's method works?

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SUMMARY

Euler's method is a numerical technique used to approximate solutions to ordinary differential equations (ODEs) by extrapolating the next point on a curve from a known starting point and the slope of the curve. This first-order method involves calculating the slope at the initial point, drawing a tangent line, and using the horizontal component of that line to determine the next point. The process is repeated iteratively to generate a series of points that approximate the curve.

PREREQUISITES
  • Understanding of ordinary differential equations (ODEs)
  • Familiarity with numerical methods and their applications
  • Basic knowledge of calculus, particularly derivatives
  • Graphical interpretation of slopes and tangent lines
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  • Study the implementation of Euler's method in Python using libraries like NumPy
  • Explore higher-order numerical methods such as Runge-Kutta
  • Learn about error analysis in numerical methods
  • Investigate applications of Euler's method in physics and engineering problems
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Students and professionals in mathematics, engineering, and computer science who are interested in numerical methods for solving differential equations.

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let's say we do not know the proof.
then how do you guys describe it conceptually?
hm...><
 
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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.
 

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