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Numerical Solution to ODE System - IVP or BVP?

  1. Mar 9, 2006 #1
    I have a system of spatial ODEs to solve... Actually a DAE system, but here's the issue:

    The equations are vaild over a specific domain, x = 0..L

    The equations are only bound at one point (thier "initial point") but at either 0 or L
    f1(0)=0
    f2(0)=100
    f3(L)=0
    f4(L)=100
    (also an algebraic expression that links all of the functions)

    Essentially, those functions bound at L are moving "backwards" with respect to those bound at 0.

    My question is, is this an initial value problem, or a boundary value problem? I started in MAPLE, and it decided (automatically) that it was a BVP. In MATLAB I am attempting to use bvp4c to come up with a solution, but is it really even a BVP if it only has one boundary condition, essentially an initial conditition, but defined at different spatial coordinates for different functions?

    Your insight is appreciated.
     
  2. jcsd
  3. Mar 9, 2006 #2

    HallsofIvy

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    Since you are given the values, of the function and its derivative, at two different points, that's a "boundary value" problem. The mathematical difference is that "existance and uniqueness", for an initial value problem, depend only on the equation. For a boundary value problem it also depends on the boundary conditions.
     
    Last edited: Mar 10, 2006
  4. Mar 10, 2006 #3
    Just to make sure I understand...

    I only have one value for each function at *one* point... (let's say L, but could be 0 for the other functions) but for the boundary at the other point (let's say 0, but other functions are not bound at 0) I can use the derivitive of the function?

    These are First order, btw.
     
  5. Mar 10, 2006 #4

    HallsofIvy

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    I don't know what you mean by "use the derivative of the function".
     
  6. Mar 10, 2006 #5
    Sorry... I need two boundary conditions for each function for a BVP, right? I only have one boundary condition per function... I thought you were saying that I could use the derivitive of the function as a boundary condition.
     
  7. Mar 11, 2006 #6

    HallsofIvy

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    What order are the equations? Typically, systems of equations are first order (any set of m nth order equations can be reduced to a system of mn first order equations). If you have have a system of 4 first order equations in 4 functions, then you need 4 conditions- exactly what you have. If you have 4 second or higher order equations then you don't have enough information. You can't "use" the derivative because you are given the derivative.
     
  8. Mar 13, 2006 #7
    All first order. I though that if I had 4 first order equations, then I would need 8 boundary conditions for both ends of the interval for each equation. I guess you're saying that is not right?
     
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