Initial value problem

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November 9th 2010, 09:14 AM
Apprentice123

Initial value problem

Solve numerically using Euler's method the following Initial value problem
$y' = 2t - e^{-2t} + 4$
$y(0) = 1$

Use an integration step equal to 0.05s, obtaining the numerical solution for five consecutive steps. Determine the analytic solution
November 9th 2010, 10:58 AM
Apprentice123

I used the formula:
$y_{j+1} = y_j +hf(x_j,y_j)$

In this case $x_j$ is $t_j$

$h = 0.05$
$y(0) = 1$
What is the value of $t_0$ ? is equal 0 ?
November 10th 2010, 02:42 PM
Apprentice123

My idea is right? What I did is right?
November 10th 2010, 11:22 PM
badgerigar

Quote:

What is the value of http://www.mathhelpforum.com/math-he...ae8f92eb09.png ? is equal 0 ?

Since $y$ is a function of $t$ , $y(0)=1$ means that when $t=0$ , $y=1$ . So yes, $t_0=0$
November 11th 2010, 12:33 PM
Apprentice123

Quote:

Originally Posted by badgerigar

Since $y$ is a function of $t$ , $y(0)=1$ means that when $t=0$ , $y=1$ . So yes, $t_0=0$

OK. Thanks

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