Hi,
by tri-diagonal matrix you mean that the derivative of variable x_i
depends only on the 3 variables x_(i-1), x_i and x_(i+1) ?
In the case of program rk, 6400 DE's do not imply that a 6400x6400
matrix will be created. The program will construct 6400 functions and a
list with 6401 elements. Each of the 6400 functions will have 6401 input
parameters (the 6400 dependent variables plus the independent variable).
With a few changes the program could be modified to construct the
functions with only 3 input parameters, picking just the 3 relevant
variables in each iteration. You might also want the program to return
only the final "point", to avoid creating large lists.
Regards,
Jaime
On 11-07-2013 16:17, herzfeld wrote:
> Hello list,
>
> For twenty years I have worked to find a mathematical model of the
> hearing system. I now am satisfied that my model works for humans.
> microchiropter and odontocetes. To implement the final piece of
> software I need to solve for the outputs, as a function of time, of
> each of 3200 inner hair cells. This is equivalent to 6400 DE's which,
> because of the geometry, form a tri-diagonal matrix.
>
> 1. At each of the 3200 IHC I have a second order DE. representing a
> "T" section of RLC components. As the index (1 - 3200) changes so do
> the values of the RLC components.
>
> 2. What is the best way to determine the individual equations for
> use in Runge-Kutta ?
>
> 3. 6400 first order DE's is a long way to go. Has anyone any ideas
> for me ?
>
> Fred
> I'm an EE not a mathematician