# Numerical Solution to ODE System - IVP or BVP?

1. Mar 9, 2006

### mpowers

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?

2. Mar 9, 2006

### HallsofIvy

Staff Emeritus
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
3. Mar 10, 2006

### mpowers

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.

4. Mar 10, 2006

### HallsofIvy

Staff Emeritus
I don't know what you mean by "use the derivative of the function".

5. Mar 10, 2006

### mpowers

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.

6. Mar 11, 2006

### HallsofIvy

Staff Emeritus
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.

7. Mar 13, 2006

### mpowers

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?