I'm currently working with a solution which is a function of many parameters, and sometimes I have to increase the steps but compromise with the time it takes for the solution to be evaluated in some way. I'm wondering, how do the steps affect the accuracy of the result?

I have some code for evaluating a velocity given different variables: > h := 50; e := 5/6; > d := .218*100; Omega := 6*Pi*(1/100); > a := -h/e; b := h/(1-e); > Q := piecewise(x <><><><><><><><><><><><><><><><><><><> k := piecewise(0 <><><><> F := 0; > tau[1] := 1/(30*d); tau[2] := (1/4)*tau[1];

I have a set of datapoints, how do I match them to a curve and obtain intercepts and extrema? Ryan

> PDE := diff(u(x, t), t) = k*(diff(u(x, t), x))+diff(u(x, t), x, x); > a := 1/70; > IBC := {u(0, t) = 0, u(5, t) = 0, u(x, 0) = exp(-(x-2.5)^2/(2*a^2))/((2*Pi)^(1/2)*a)}; > pds := pdsolve(PDE, IBC, numeric, time = t, range = 0 .. 5, timestep = 1/2000, spacestep = 1/2000); >R := pds:-value(output = listprocedure); >uu := subs(R, u(x, t))

I'm solving a differential equation in a region of appearing and disappearing potential energy, hence there is a piecewise function in the PDE w.r.t. time. The potential disappears randomly, and I need to generate a set of random times about a mean that I can put into the piecewise function to achieve this. What is the best way of generating random numbers modelled by a Poisson distribution so they can be fed into a function? Any help appreciated, Ryan