- #1
pysox
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Hello
I need to plot this simple system:
x'' = -x
using midpoint Euler.
u1 = -x , u2 = -x'
u1' = u2
u2' = -x
u1(n+1) = u1(n) + h*?
u2(n+1) = u2(n) + h*f((1/2)*(u1(n) + u1(n+1))
We don't know u1(n+1). I tried approximating it with u1(n+1) = u1(n) + h*u2(n)
u2(1+i) = u2(i) + h * ((-1/2) * (u1(n) + u1(n+1))
Then we have u2(i+1) and u2(i). A midpoint value is (u2(1+i) - u(i))/2
u1(q+i) = u1(i) + h*midpoint
When i plot this the result is some awful diverging line, not an oscillating function. What is wrong?
I need to plot this simple system:
x'' = -x
using midpoint Euler.
u1 = -x , u2 = -x'
u1' = u2
u2' = -x
u1(n+1) = u1(n) + h*?
u2(n+1) = u2(n) + h*f((1/2)*(u1(n) + u1(n+1))
We don't know u1(n+1). I tried approximating it with u1(n+1) = u1(n) + h*u2(n)
u2(1+i) = u2(i) + h * ((-1/2) * (u1(n) + u1(n+1))
Then we have u2(i+1) and u2(i). A midpoint value is (u2(1+i) - u(i))/2
u1(q+i) = u1(i) + h*midpoint
When i plot this the result is some awful diverging line, not an oscillating function. What is wrong?