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Euler expansion of double exponential?

  1. Feb 5, 2008 #1
    Simple question,

    I have used the euler expansion to estimate a variable that grows as a single exponential.
    adapt = Amax * exp(-tau*X);

    In excerpted form:

    for (i=1;i<npts; i++)
    adapt = adapt[i-1] + (Amax -adapt[i-1]) * dt / tau;

    where dt is the step size and tau is the 'time constant.'

    Now, however, I think that the data would be better fit with a double exponential.

    adapt = a(1) * exp(-tau1*X) + a(3) * exp(-tau2*X);

    I am unsure how to expand this analogously to the single exponential.

  2. jcsd
  3. Feb 7, 2008 #2
    Assuming that a(1) and a(3) are some incremental values, you can define your system as an autonomous system as, [tex]\dot{x} = Ax[/tex] where [tex]A[/tex] is a [tex]3 \times 3[/tex] matrix and [tex]x \in \mathbb{R}^3[/tex], then expand the matrix exponential. And take the first state.
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