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Help about the numerical computation on the following equations

  1. Oct 17, 2007 #1
    Dear every memeber, I encountered the numerical computation on the following
    differential equations. I use four-step Runge-Kutta methods to integrate, but
    the result is not converge, even if I take the time step (t=0.0001).
    please help me why so? Could you please tellme which Fortran subroutine can do the tasks? (I know the following equations has exact solutions.)

    [tex]i\frac{dy_1}{dt}=20.0y_2; \\ i\frac{dy_2}{dt}=20.0y_1[/tex]
     
  2. jcsd
  3. Oct 18, 2007 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    What do you mean by "converge"? Runge-Kutta gives a specific result, there is no "convegence" involved. Or do you mean "converge, as the time step gets smaller, to the answer I get by integrating directly"?
     
  4. Oct 18, 2007 #3

    J77

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    Why the "i"?
     
  5. Oct 18, 2007 #4
    "i" is the imaginary unit.
    I tried Runge-Kutta in IMSL, and code in the well-known book 'numerical recipe'.
    They can not give the correct result. The original equations are 2500 differential equations looking like this
    [tex]i\frac{dp_{ij}}{dt}=-50*(p_{i+1,j}+P_{i-1,j})+50*(p_{i,j-1}+P_{i,j+1})))-ip_{ij}/5 [/tex]
    i,j=1,2,..50.

    Please help me, Dudes.

    I can not obtained the correct numerical result.
     
  6. Oct 19, 2007 #5
    Does not look very bad. I think you should first write the equations in the form that does not involve i-s.
     
  7. Oct 19, 2007 #6
    Thank you, timur, J77 , Hallsofivy

    +50 should be -50.
    The problem is that it is high oscillatory, I can obtained the numerical result when
    i=1,2,3, and j=1,2,3. when i is larger than 3, the numerical result start to diverge.
    That is very tricky

    the correct equations should be

    [tex]i\frac{dp_{m,n}}{dt}=-50\times[(p_{m-1,n}+p_{m+1,n})+(p_{m,n-1}+p_{m,n+1})]-ip_{mn}/5[/tex]

    i is the the imaginary unit
     
  8. Oct 19, 2007 #7
    I solved it.
     
    Last edited: Oct 20, 2007
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