This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: GE 207K Euler’s Method – Overview September 19, 2011 Notes : 1. Below are my notes on Euler’s method that I wrote couple years back. I’m resorting to a graphical explanation in these notes. Looking back, I could have provided a better explanation. Please come see me during my office hours if you’d like to see my alternative explanations. 2. What I’m describing is really “Explicit Euler” (aka. Forward Euler) which I simply refer to as “Euler Method”. It’s counterpart, “Implicit Euler” (aka Backward Euler) is more stable, but computationally more expensive. Overview of Euler’s method : Let’s start out with an Initial Value Problem (IVP) written in the following form which we will take to be the standard form for using Euler’s method: y 1 f p x,y q (1) y p x q y (initial condition) From the given IVP, we know two things: 1. Value of y at x . (which is y ) 2. The slope of the solution at point p x ,y q . We will use the above information to approximate the solution to the initial value problem. By plugging p x ,y q in to Eq. ( 1 ), we find the initial slope S . Now study the figure below carefully....
View Full Document