- #1
narayanjr
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Homework Statement
In aerodynamics, one encounters the following initial value problem for Airy’s equations:
y''(x) + xy = 0, y(0) = 1, y'(0) = 0
Using the Runge-Kutta method with h=0.005 and determine values between x=0 and x=10 sufficient to sketch the relationship.
Homework Equations
y''(x) + xy = 0, y(0) = 1, y'(0) = 0
I think,
k1 = h*f(Xn, Yn)
k2 = h*f(Xn+h/2, Yn+k1/2)
k3 = h*f(Xn+h/2, Yn+k2/2)
k4 = h*f(Xn + h, Yn + k3)
The Attempt at a Solution
From what I have read you can't do second order ODE using runge kutta without breaking it into a system of first order ODEs so that's what I tried.
I tried:
d2y/dx2 + xy = 0
dy/dx = z, y(0) = 1
dz/dx + xy = 0
dz/dx = -xy, z(0) = 0
I don't know if that is right or not and if it is I have no idea where to go from here.
Thanks for any help.