Euler's method

  • Thread starter leopard
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  • #1
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[tex]y_{2,n} + 0.1(2y_{2,n} - y_{1,n} + 4t)[/tex]

If [tex]y_{1,0}=1[/tex] and [tex]y_{2,0}=1[/tex], what is [tex]y_{2, 0.1}[/tex]?

1.1 or 1.14?
 

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  • #2
HallsofIvy
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Your notation is a bit confusing. Normally an index "n" refers to integer values. What is it here? In other words, what does y2,0.1 mean? Also there is no equation. What is that expression supposed to be equal to? And, finally, what is "t" here?
 
  • #3
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x'' - 2x' + x = 4t, x(0) = 1, x'(0)=1

Introducing [tex]y_1 = x[/tex] and [tex]y_2 = x'[/tex]

we have the system

[tex]y_1 ' = y_2[/tex]

[tex]y_2 ' = 2y_2 - y_1 + 4t[/tex]

right?

Using Euler's method with step size h=0.1, we get

[tex]y_{1, n+1} = y_{1, n} + 0.1y_{2,n}[/tex]

[tex]y_{2,n + 1} + 0.1(2y_{2,n} - y_{1,n} + 4t)[/tex]

It's easy to see that [tex]y_{1, 1} = 1 + 0.1 \cdot 1 = 1.1[/tex], but what is [tex]y_{2,1}[/tex]?
 
Last edited:

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