Crank-Nicolson is much less accurate than implicit FTCS.

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I am worried about this. I am solving the heat equation with α=1 and homogeneous Dirichlet boundary conditions. I use dt=0.00001, dx=0.01, nx=101 in the interval [0,1]. I found that the implicit FTCS gives me an error (difference between the analytic solution and the numerically computed solution) between 0 and 0.006. The C-N method for exactly the same problem gives me an error between 0 and 0.14. That is about two orders of magnitude larger in C-N. I expected higer precision in C-N. Any idea why is this happening? I evaluated the error in times 0.1,0.2,0.3,0.4,0.5. I have
graphs for this with $x in [0,1]$ with $dx=0.01$. All is done in Python.



I appreciate any suggestion about this (other than telling me I have a bug in my code. I seriously consider this as an option and I am looking into this, but I cannot yet find a bug).



When I use $dt=0.1$ C-N is more accurate than FTCS. Errors in C-N in $[-0.12,0.3]$ and FTCS $[0,0.8]$.



Thanks.




pde numerical-methods




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  • A better site for this question would be scicomp.stackexchange.com.
    – Mattos
    Aug 26 at 23:14










  • @Mattos: Thanks for your suggestion. I will post it there. I guess I can include Python code there, right?
    – Herman Jaramillo
    Aug 27 at 1:43






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    Yes, you can include your code there.
    – Mattos
    Aug 27 at 2:43














up vote
1
down vote

favorite
1












I am worried about this. I am solving the heat equation with α=1 and homogeneous Dirichlet boundary conditions. I use dt=0.00001, dx=0.01, nx=101 in the interval [0,1]. I found that the implicit FTCS gives me an error (difference between the analytic solution and the numerically computed solution) between 0 and 0.006. The C-N method for exactly the same problem gives me an error between 0 and 0.14. That is about two orders of magnitude larger in C-N. I expected higer precision in C-N. Any idea why is this happening? I evaluated the error in times 0.1,0.2,0.3,0.4,0.5. I have
graphs for this with $x in [0,1]$ with $dx=0.01$. All is done in Python.



I appreciate any suggestion about this (other than telling me I have a bug in my code. I seriously consider this as an option and I am looking into this, but I cannot yet find a bug).



When I use $dt=0.1$ C-N is more accurate than FTCS. Errors in C-N in $[-0.12,0.3]$ and FTCS $[0,0.8]$.



Thanks.




pde numerical-methods




share|cite|improve this question




















  • A better site for this question would be scicomp.stackexchange.com.
    – Mattos
    Aug 26 at 23:14










  • @Mattos: Thanks for your suggestion. I will post it there. I guess I can include Python code there, right?
    – Herman Jaramillo
    Aug 27 at 1:43






  • 1




    Yes, you can include your code there.
    – Mattos
    Aug 27 at 2:43












up vote
1
down vote

favorite
1









up vote
1
down vote

favorite
1






1





I am worried about this. I am solving the heat equation with α=1 and homogeneous Dirichlet boundary conditions. I use dt=0.00001, dx=0.01, nx=101 in the interval [0,1]. I found that the implicit FTCS gives me an error (difference between the analytic solution and the numerically computed solution) between 0 and 0.006. The C-N method for exactly the same problem gives me an error between 0 and 0.14. That is about two orders of magnitude larger in C-N. I expected higer precision in C-N. Any idea why is this happening? I evaluated the error in times 0.1,0.2,0.3,0.4,0.5. I have
graphs for this with $x in [0,1]$ with $dx=0.01$. All is done in Python.



I appreciate any suggestion about this (other than telling me I have a bug in my code. I seriously consider this as an option and I am looking into this, but I cannot yet find a bug).



When I use $dt=0.1$ C-N is more accurate than FTCS. Errors in C-N in $[-0.12,0.3]$ and FTCS $[0,0.8]$.



Thanks.




pde numerical-methods




share|cite|improve this question












I am worried about this. I am solving the heat equation with α=1 and homogeneous Dirichlet boundary conditions. I use dt=0.00001, dx=0.01, nx=101 in the interval [0,1]. I found that the implicit FTCS gives me an error (difference between the analytic solution and the numerically computed solution) between 0 and 0.006. The C-N method for exactly the same problem gives me an error between 0 and 0.14. That is about two orders of magnitude larger in C-N. I expected higer precision in C-N. Any idea why is this happening? I evaluated the error in times 0.1,0.2,0.3,0.4,0.5. I have
graphs for this with $x in [0,1]$ with $dx=0.01$. All is done in Python.



I appreciate any suggestion about this (other than telling me I have a bug in my code. I seriously consider this as an option and I am looking into this, but I cannot yet find a bug).



When I use $dt=0.1$ C-N is more accurate than FTCS. Errors in C-N in $[-0.12,0.3]$ and FTCS $[0,0.8]$.



Thanks.





pde numerical-methods





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asked Aug 26 at 22:51









Herman Jaramillo

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  • A better site for this question would be scicomp.stackexchange.com.
    – Mattos
    Aug 26 at 23:14










  • @Mattos: Thanks for your suggestion. I will post it there. I guess I can include Python code there, right?
    – Herman Jaramillo
    Aug 27 at 1:43






  • 1




    Yes, you can include your code there.
    – Mattos
    Aug 27 at 2:43
















  • A better site for this question would be scicomp.stackexchange.com.
    – Mattos
    Aug 26 at 23:14










  • @Mattos: Thanks for your suggestion. I will post it there. I guess I can include Python code there, right?
    – Herman Jaramillo
    Aug 27 at 1:43






  • 1




    Yes, you can include your code there.
    – Mattos
    Aug 27 at 2:43















A better site for this question would be scicomp.stackexchange.com.
– Mattos
Aug 26 at 23:14




A better site for this question would be scicomp.stackexchange.com.
– Mattos
Aug 26 at 23:14












@Mattos: Thanks for your suggestion. I will post it there. I guess I can include Python code there, right?
– Herman Jaramillo
Aug 27 at 1:43




@Mattos: Thanks for your suggestion. I will post it there. I guess I can include Python code there, right?
– Herman Jaramillo
Aug 27 at 1:43




1




1




Yes, you can include your code there.
– Mattos
Aug 27 at 2:43




Yes, you can include your code there.
– Mattos
Aug 27 at 2:43















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