[Maxima-discuss] Numerical Integration of Numerical Data

[Daniel V. <dan...@ya...>]

Hi All,
Given a numerical calculation like the result of rk, rkf45 or Eulix, I would like to obtain the numerical integral function of the result.The input is a list of lists, each sublist of equal length. The first element of each sublist is monotonically increasing, modeling time (t) or arc-length (s).The other elements of the sublist model smooth functions.
My attempts have been successful but extremely wasteful. I interpolate the entire input data and convert it to a function. Then I calculate the numerical value of the integral with respect to time at each point.
load(rkf45)$load(interpol)$load(grobner)$
rksol:rkf45([x*(1-y),-y*(1-x)],[x,y],[2,2],[t,0,10,0.01],
           absolute_tolerance=5E-8,report=true)$
plot2d([[discrete,map(lambda([u],part(u,[1,2])),rksol)],
          [discrete,map(lambda([u],part(u,[1,3])),rksol)]],
         [style,[lines,2]],[y,0,3])$
Lx:map(lambda([u],part(u,[1,2])),rksol)$
Ly:map(lambda([u],part(u,[1,3])),rksol)$
linearinterpol(Lx,varname='t)$ Fx(t):=''%$
linearinterpol(Ly,varname='t)$ Fy(t):=''%$
plot2d([Fx(t),Fy(t)],[t,0,10],[style,[lines,2]],[y,0,3])$
Ix:makelist([i,romberg(Fx(t),t,0,i)],i,0,10,0.01)$
Iy:makelist([i,romberg(Fy(t),t,0,i)],i,0,10,0.01)$
plot2d([[discrete,Ix],[discrete,Iy]],[style,[lines,2]])$
Did anyone solve this problem before?Is there a Maxima package that solves this problem?Any suggestions?
Thanks,
Daniel