Symbolically solving Wikipedia RungeKutta example?by honglin Tags: rungekutta, solving, symbolically, wikipedia 

#1
May712, 05:51 PM

P: 1

The Wikipedia page for "RungeKutta methods"[1] gives the following example:
y' = tan y + 1 y(1) = 1 t in [1, 1.1] Using a stepsize 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.[2] So I'm wondering if this simplelooking DE actually has a symbolic solution? Notes: [1] wikipedia (dot) org/wiki/Runge%E2%80%93Kutta_methods [2] 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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