integration function

[Paul Thomas]

Just to expand the replies a bit further;

Take a simple example  y(s) = integral( 2*t*exp(-t^2) ) [0 to s]

1] with quad-
octave:1> function dydt = mz(t);dydt=2*t*exp(-t*t);endfunction
octave:2> quad("mz",0,[1,2])
ans = 0.63212

2] the analytic solution = ( 1 - exp( -s*s ))
octave:3> 1-exp(-1*1)
ans = 0.63212

3] with LSODE
octave:4> function dydt = mf(y,t);dydt=2*t*exp(-t*t);endfunction
octave:5> t=[0,1];[a,b,c]=lsode("mf",0,t);a(2)
ans = 0.63212

Note that the function for lsode has as inputs the dependent 
variable(y), which is unused here and the independent variable(t).

4] Getting a bit perverse, a tiny bit of algebra gives:
y(s) = integral( 2*t*y(t) ) [0 to s], so using LSODE again:

octave:6> function dydt = mg(y,t);dydt=2*t*(1-y);endfunction
octave:7> t=[0,1];[a,b,c]=lsode("mg",0,t);a(2)
ans = 0.63212

quad is about 4 times faster than lsode for this application, with 
default accuracies.  However, if you want to tabulate intermediate 
values by putting more values in the input t-vector, the execution time 
of lsode barely changes, whereas quad must be put in a loop (I think?).

This time using dependent and independent variables.

Paul T



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