Levenberg-Marquardt on differential equation

Hello,

I am using Levenberg-Marquardt optimizer to minimize a function with
two unknowns.

X(t) and Y(t) are my discretized signals which relates following this
equation:

Y'(t) = A*X(t) - B*Y(t) (1)

Obviously Y(t) is in the form

Y(t) = A * Integral( X(t') * exp( -B * (t - t') dt' ) (2)

If I setup the optimizer to minimize the difference in between the
discretized Y(t) and (2), everything seems to converge nicely. However
calling 'exp' in my C++ program is prohibitively slow, and I thought
of directly using (1) in the optimizer. But things do not converge
nicely. Is there something obvious why not to use (1) directly ? All I
care really it the optimized A and B parameters.

To approximate Y'(t) I am using the following expression (five point
method):

http://en.wikipedia.org/wiki/Numerical_differentiation#Higher_order_methods

thanks for input,
-Mathieu

.

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