- #1
memarf1
- 18
- 0
Im trying to turn this equation into 2 separate equations in order to place it in a runge kutta problem. This is the proposed problem and conditions:
[tex]\frac{d^2f}{dx^2} + f = 0[/tex]
allowing
[tex]f (x) = A\cos x + B\sin x[/tex]
[tex]f ' (x) = -A\sin x + B\cos x[/tex]
[tex]f '' (x) = -A\cos x - B\sin x[/tex]
and
[tex]g = \frac{df}{dx}[/tex]
meaning
[tex]\frac{df}{dx} - g = 0[/tex] which is identical to [tex]\frac{d^2f}{dx^2} + f = 0[/tex]
so
[tex]\frac{dg}{dx} + f = 0[/tex]
the initial conditions for equation 1 are:
[tex]f (0) = 1[/tex]
[tex]f ' (0) = 0[/tex]
and for equation 2 are:
[tex]f (0) = 0[/tex]
[tex]g (0) = 1[/tex]
I hope this formatting is more easy to read.
any suggestions??
[tex]\frac{d^2f}{dx^2} + f = 0[/tex]
allowing
[tex]f (x) = A\cos x + B\sin x[/tex]
[tex]f ' (x) = -A\sin x + B\cos x[/tex]
[tex]f '' (x) = -A\cos x - B\sin x[/tex]
and
[tex]g = \frac{df}{dx}[/tex]
meaning
[tex]\frac{df}{dx} - g = 0[/tex] which is identical to [tex]\frac{d^2f}{dx^2} + f = 0[/tex]
so
[tex]\frac{dg}{dx} + f = 0[/tex]
the initial conditions for equation 1 are:
[tex]f (0) = 1[/tex]
[tex]f ' (0) = 0[/tex]
and for equation 2 are:
[tex]f (0) = 0[/tex]
[tex]g (0) = 1[/tex]
I hope this formatting is more easy to read.
any suggestions??
Last edited: