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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?

- Thread starter leopard
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- #1

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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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HallsofIvy

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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]?

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]?

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