Advanced Engineering Mathematics: Euler Method

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Homework Help Overview

The discussion revolves around solving a differential equation using the Euler method. The specific problem involves the equation y' = (y - x)² with the initial condition y(0) = 0 and a step size of h = 0.1. Participants are exploring the exact solution and the error associated with the numerical method.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express confusion about obtaining the exact solution and the steps to take from the given differential equation. There are discussions about the nature of the equation being non-linear and the potential use of Taylor series to understand error bounds. Some participants question the relevance of Taylor series in their current learning context.

Discussion Status

The discussion is ongoing, with participants sharing hints and exploring different interpretations of the problem. Some guidance has been provided regarding rewriting the equation in terms of a new variable, but there is no explicit consensus on the approach to take.

Contextual Notes

Participants note that the problem specifies performing 10 steps, although some believe fewer steps may suffice. There is uncertainty about the exact solution and the applicability of Taylor series in their current studies.

think4432
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Do 10 steps. Solve the problem exactly. Compute the error (Show all details).

The problems says do 10 steps, but 3-4 steps will suffice!

Problem: y(prime) = (y-x)^2
y(0) = 0
h = 0.1

I don't understand how to get the exact solution and what to do from there!
I know that,
f(x,y) = (y-x)^2

And that u = (y-x)

But from there, I am stuck!

Help!
 
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The differential equation can be solved. However it's not a very obvious solution since it is not linear.

However you can get a bound on the error if you think about the problem in terms of Taylor series. Specifically what's the difference in using Euler's method versus a Taylor series?
 
Feldoh said:
The differential equation can be solved. However it's not a very obvious solution since it is not linear.

However you can get a bound on the error if you think about the problem in terms of Taylor series. Specifically what's the difference in using Euler's method versus a Taylor series?

I don't think we're learning about Taylor series, but I just don't understand how we would solve the DE...

I can probably apply to Euler's method after solving it...
 
Hint: What is u' equal to? Rewrite the original differential equation in terms of u.
 

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