I would appreciate help with how to get a value using Richardson extrapolation. This is the question I have:
Calculate $\int^{1/2}_{0}e^x$... (a) to a six decimals, by determing the primitive function (b) with the trapezoidal rule, step length h=$\frac{1}{4}$ and (c) using extrapolation to h=o on the result which one gets with h=$\frac{1}{2}$,$\frac{1}{4}$.
I have the gotten the correct answers for (a) 0.648721 and (b) 0.652096 but how do I solve c?
From my study book I can find the formula for extrapolation: $T(h)+\frac{1}{3}((T(h)-T(2h))$, and I tried using this for $T(h)=T(\frac{1}{8})$ and $T(2h)=T(\frac{1}{4})$. But got the wrong answer, I got 0.648722 (0.64872214895) but according to the results, the answer should be 0.648735.
I have also tried with $T(h)=T(\frac{1}{4})$ and $T(2h)=T(\frac{1}{2})$ but neither that gives the right answer.
What am I doing wrong?
