Euler's method

1. Dec 11, 2008

leopard

$$y_{2,n} + 0.1(2y_{2,n} - y_{1,n} + 4t)$$

If $$y_{1,0}=1$$ and $$y_{2,0}=1$$, what is $$y_{2, 0.1}$$?

1.1 or 1.14?

2. Dec 11, 2008

HallsofIvy

Staff Emeritus
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. Dec 11, 2008

leopard

x'' - 2x' + x = 4t, x(0) = 1, x'(0)=1

Introducing $$y_1 = x$$ and $$y_2 = x'$$

we have the system

$$y_1 ' = y_2$$

$$y_2 ' = 2y_2 - y_1 + 4t$$

right?

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

$$y_{1, n+1} = y_{1, n} + 0.1y_{2,n}$$

$$y_{2,n + 1} + 0.1(2y_{2,n} - y_{1,n} + 4t)$$

It's easy to see that $$y_{1, 1} = 1 + 0.1 \cdot 1 = 1.1$$, but what is $$y_{2,1}$$?

Last edited: Dec 11, 2008