- #1

meddi83

- 3

- 0

## Homework Statement

Hi guys, I have the following problem and I don't know how to start.

I am given that W = 0.5, X(0) = 0, Iab = 20m and ha = 5m [tex]\frac{dy}{dx}=0[/tex]

and

[tex]

\frac{dy^2}{d^2x}=\frac{W}{T}\sqrt{1 + (\frac{dy}{dx})^2}

[/tex]

I am told to convert the 2nd order ODE to two 1st order ODEs at first. Then I am asked to choose an arbitrary value of T and integrate the system of equations using Euler's method from 0-Iab, where Iab=20, with 3 different step sizes. Then, I have to select the step size that gives an accurate value of y(Iab) (i.e. approximate relative error less than 0.1% if comparing with ha = 5).. Then I am asked to chose two values of T such that one gives y(Iab) smaller than ha and the other one gives y(Iab) bigger than ha and use those two values with the bisection method

## Homework Equations

Euler's method: [tex]yi+1 = yi + f(xi,yi)*h[/tex] where [tex]f(x,y) = \frac{dy}{dx}[/tex]

## The Attempt at a Solution

At first I broke it to two 1st order ODES:

[tex]\frac{dy}{dx}=g[/tex] and [tex]\frac{dg}{dx}=\frac{W}{T}\sqrt{1 + g^2}[/tex]

Then, for Euler's method: [tex]yi+1 = yi + gi*h[/tex] and [tex]gi+1 = gi + (\frac{W}{T}\sqrt{1+gi^2})*h[/tex]

My problem is, I don't know where to start in order to find y(Iab) (because the problem is asking for an accurate value of y(Iab) )... and what step size (h) to use. .. I also don't know which equation shall be used with the bisection method..

any help would be really appreciated. thank you