Author 
Comment/Response 
Charlie Brummitt

06/27/06 11:56am
I would like to be able to add 1 (or any other number) to an interpolating function and then set that interpolating function to that new function. For example, I'd like to do something like this:
(* suppose 'solution' is an interpolating function generated by NDSolve *)
solution = solution + 1;
Is there a way to do this? The reason I want to do this is because I am trying to write code for calculating the Lyapunov exponent in order to test PDE's for chaos. I want to "perturb" the solution (which is an interpolating function) at every timestep as NDSolve solves the PDE.
Here's what I'm trying to do:
First, I solve the PDE, and I call this the unperturbed solution. Then I solve it again but with a tiny perturbation. Rather than doing just one perturbation at the beginning, I do a perturbation at each timestep but keep bringing the perturbed solution "back" to the unperturbed solution. In other words, at each timestep in the evolution of NDSolve, I reset the perturbed solution to where the unperturbed solution is, and then I perturb it slightly. (The reason I do this is because I don't want the two solutions to spread further and further apart. This way I can calculate the degree to which nearby intial conditions spread apart and keep reorienting the perturbed solution to where the unperturbed solution is.)
Essentially, what I want to do when I solve the perturbed solution is to have a step monitor that does the following:
StepMonitor :>
(*code to store the local lyapunov exponent, already written and working*);
AppendTo[listOfExponents, Log[Abs[u[pos, t]  unperturbedSolution[pos,
t]]/?R]];
(*now the troublesome part: reset the perturbed solution back to where the unperturbed solution is at this point in time t but then perturb it by ?R *)
(*this is the code I want to be able to write, but it doesn't seem to work *)
u[x, t] = unperturbedSolution[x, t] + ?R;
(*note: the unperturbedSolution has already been solved previously, so I have that solution  an interpolating function  at my disposal. *)
Essentially, how can I set an interpolating function to another interpolating function + some number (like .00000001)?
I tried making a new interpolating function from data generated using the old interpolating function:
u[x, t] = Interpolation[Table[?R + unperturbedSolution[x, t],{x, 0, length, 1}]]
...but this didn't seem to work either. Plus, it would be slow if it did.
Is there any way to do this? If someone could give me some help I would greatly appreciate it.
URL: , 
