|May7-12, 05:51 PM||#1|
Symbolically solving Wikipedia Runge-Kutta example?
The Wikipedia page for "Runge-Kutta methods" gives the following example:
y' = tan y + 1
y(1) = 1
t in [1, 1.1]
Using a step-size of h = .025, this solution is found:
y(1.1) = 1.335079087
I decided to check this solution by solving symbolically. But my attempts to symbolically integrate only lead to more complicated equations. So I'm wondering if this simple-looking DE actually has a symbolic solution?
 wikipedia (dot) org/wiki/Runge%E2%80%93Kutta_methods
 For example,
y'(t) = tan(y(t)) + 1
y'(t)/(tan(y(t)) + 1) = 1
Let u = y(t), du = y'(t) dt
∫(du/(tan(u) - 1)) = ∫dt
I used the SAGE computer algebra system to evaluate the LHS to,
-1/2*u + 1/2*log(tan(u) - 1) - 1/4*log(tan(u)^2 + 1)
Not much help!
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