hi, chi:
in the splint function inside of Numerical.h, there is the following line
for implementing trapezoidal numerical integration:
s += (hi/2.0) * (y[i]+y[i+1] - (hi*hi/12.)*(y2[i]+y2[i+1]));
the first contribution is the trapezoidal area; the second is the error
term, i assume. am i interpreting this right?
if so, is this formula correct? my reference says that the error term for
the trapezoidal rule is:
err = - h1 * h1 * h1 * y2[c] / 12.0
where c is the value such that y2[c] is maximum on the interval. i wonder
about the relevance of taking the end-point average second derivative and
assuming that this is the maximum.
also, can you even add the error term like this? doesn't the error
derivation require an absolute value sign:
abs( int(f(x),x=a,b) - trap(f(x),x=a,b) ) < err
aaron
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