@k20057 5 There are only two parameters, and hence only two equations.

f:= E-> exp(-E/kT)/A:
eq1:= f(0) = ...:
eq2:= f(1) = ...:
....

@k20057 5 The system of equations cannot be solved with independent solutions for A and B because B/A is essentially a single coefficient.

What version of Maple are you using? Maple 18 accepts your code, and the unapply changes x[2] to x_2, which shouldn't make any difference because it is a dummy variable.

The equations are missing from your Question. Try including them in plain text form, or try attaching a worksheet.

The worksheet attachment of your post is missing. Please try uploading and attaching again.

What exactly is in the Excel worksheet? Is it just a column of 200 or so numbers? Or does it have the variable name also? Is the issue that you want to match a list of 200 or so values with a list of 200 or so variables? That can be done fairly easily.

@lasseledet Give me the values of the parameters and I'll try to find something.

You said that the root that you want is close to -1+I. You can use RootFinding:-Analytic with the range being a box centered at -1+I.

You could let k = x+I*y, then use DirectSearch:-SolveEquations on Re(DispersionEq) and Im(DispersionEq).

@lasseledet Do you have numeric values for Omega, Zeta, lambda, nu, rho, and gamma__o? Without numeric values, I think that it is hopeless. With numeric values, I think that it will be easy with fsolve or another root finder.

@Mac Dude My reading is that by "export" the OP means to write out the values so that they can be read by another program. For that, we need to know the format that the other program accepts.

In this post, Samir Khan does it by using a textplopt on each contour.

It is not clear to me what you mean by the minus sign in f^-2. Do you mean something having to do with an inverse function? From your subsequent code, it looks like you intended merely the second derivative. But why the minus sign?

What do you hope to achieve from a symbolic solution to this problem that you can't get from a numeric solution? Maybe we can show you how to get it from the numeric solution. The symbolic solution is unwieldy, and I doubt that it can be significantly improved.

@acer 

solve(x^2 - 2*(m+1)*x+m^2 - 2*m + m^2=0,{x},real,parametric=full);

As one small step towards the goal, I'll point out that one of the fundamental data structures required for the algorithm---a priority queue---is implemented in Maple via the ancient and little-known command priqueue.

@Mac Dude 

Good answer. Would you kindly please provide an example of what you mean by "series will not work on functions"? It's not that I doubt what you say; I just don't understand it.

@casperyc Sorry that I didn't see your comment earlier.

You asked:

I am a bit confused why (how) would you  think of reducing the accuracy?

Why: Because the error message that one gets when using the default accuracy suggests that an answer may be possible at a reduced accuracy, and it even suggests what to reduce the accuracy to.

Sol:= dsolve({ODE, BCs}, numeric, method= bvp[middefer], maxmesh= 2^15);

Error, (in dsolve/numeric/bvp) unable to achieve requested accuracy of 0.1e-5 with maximum 32768 point mesh (was able to get 0.14e-2), consider increasing `maxmesh` or using larger `abserr`

How: By adjusting the parameters relerr and/or abserr.

And what does the Reduced accuracy answer tell us?

Nothing in this case. In some other case it may be the only way to get an answer, and the answer produced will be accurate to the given accuracy.

In my experience, sometimes when I got underflow (tooo small) issue, I would increase accuracy, to get something out of it.

Numeric solution of BVPs is much trickier than IVPs. It is difficult to increase the accuracy without increasing the mesh size, and the maximum mesh size is 2^15. Larger mesh sizes mean a larger system of linear equations to solve, which introduces its own accuracy problems.