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CrankNicolson vs Heun's method 
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#1
Apr610, 09:49 AM

P: 30

Hi, can someone tell me the difference between the CrankNicolson and Heun numerical methods? For Heun's method I'm looking here http://en.wikipedia.org/wiki/Heun%27s_method and for the CrankNicolson method I'm looking here http://en.wikipedia.org/wiki/Crank%E...icolson_method . When I actually carry out a calculation with equal timesteps for both methods and f(t,u)=.5*u, I get the exact same solution.
The equation I have for both is: u[tex]^{n+1}[/tex] = u[tex]^{n}[/tex]  [tex]\frac{1}{2}[/tex]u[tex]^{n}[/tex]dt  [tex]\frac{1}{8}[/tex]u[tex]^{n}[/tex]dt[tex]^{2}[/tex] 


#2
Apr910, 10:02 AM

P: 88

I'm no expert, but from what I can gather Heun's method is for ODE's while CrankNicolson is for PDE's?



#3
Apr910, 10:39 AM

P: 333

Heun's method is an improvement of the forward Euler's method which is an explicit method.
While CrankNicolson method is an implicit method. Probably the improvement for the backward Euler method. This is the CrankNicolson method for ODE. But of course the CrankNicolson method is verypopular in PDE. 


#4
Apr1010, 09:46 AM

P: 88

CrankNicolson vs Heun's method
Ah, in all cases I've come across CrankNicolson, it has been to solve PDEs.
So, if I read my notes correctly, while both methods take an average of the current state and the state at the next timestep, the main difference between Heun's method and CrankNicolson is that for Heun's method you use a predictor for the next timestep, keeping it explicit, while for CrankNicolson it is used implicitly instead. At least that's my understanding. Using this I get some different results from yours, both with CrankNicolson and Heun's method, are you sure you do Heun's method correctly? 


#5
Apr1010, 05:57 PM

Mentor
P: 12,068

For CrankNicolson, ignore the xdependence of u and we have (u^{n+1}  u^{n}) / Δt = ½ ( ½ u^{n+1}  ½ u^{n})Solve that for u^{n+1} and we get something different than the Heun's method equation. (Though they do agree up to order Δt^{2}.) 


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