Euler's Numerical Method for y'=f(x,y) and its Generalizations
In this lesson, students are introduced to Euler's method, a basic numerical method for solving differential equations. The method involves finding the slope of the line element at the starting point, choosing a step size, and continuing the solution until reaching the next point. The lesson includes an example of using Euler's method to solve a non-trivial differential equation, and also discusses the limitations of the method and how to determine if the solution curve is convex or concave.
Euler's Numerical Method for y'=f(x,y) and its Generalizations -- Lecture 2. How to find numerical solutions to differential equations.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 23, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
- Lecture Notes - Lecture Notes
- Notes - Notes and exercises written by Prof. Mattuck
- Recitation Problems - Recitation Problems and classwork exercises
- Recitation Solutions - Recitation problem solutions
- Euler's Method Java Applet - Interactive Java Applet to learn and discover Euler's Method.
- How are differential equations solved in real life?
- What is Euler's numerical method for solving differential equations?
- How do you solve a differential equation numerically?
- What is an initial value problem?
- What is an IVP?
- What are Euler's Equations?
- What is the Runge-Kutta 4th order method?
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Staff Review
This video does a great job of explaining Eulerâs method for finding numerical solutions to differential equations. This is a very practical and useful way of solving differential equations. -
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