Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
    thanks!

    Clifford
     
  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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Euler expansion of double exponential?
  1. Euler method (Replies: 12)

  2. Euler's method (Replies: 5)

  3. Euler equation (Replies: 1)

  4. Euler's Method (Replies: 3)

  5. Euler D.E. (Replies: 2)

Loading...