@@ -16,7 +16,8 @@ where $h := x_2 - x_1 = x_1 - x_0$ is the width of one slice. Note that the erro
I = \int_{-1}^{1} e^{-x^2} dx.
\end{equation}
You may use the following SciPy functions: \href{https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.trapezoid.html#scipy.integrate.trapezoid}{\texttt{scipy.integrate.trapezoid}} and \href{https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.simpson.html#scipy.integrate.simpson}{\texttt{scipy.integrate.simpson}}. % and \href{https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.romb.html}{\texttt{scipy.integrate.romb}}.
\item Repeat the calculation using three different values of $h$. Plot the error $\Delta I$ against $h$. Show that the numerical estimates converge to the exact value according to the expected order of convergence. To show this, you can plot the error [which will be $\mathcal(O)(h^n)]$ against $h$ as a log-log plot and look at the slope.
\item Repeat the calculation using three different values of $h$. Plot the error $\Delta I$ against $h$. Show that the numerical estimates converge to the exact value according to the expected order of convergence. First, you can plot the error [which will be $\mathcal(O)(h^n)]$ against $h$ as a log-log plot and look at the slope. This will give you an idea of the order of convergence $n$. Then, you can actually compute $n$ using Eq.\eqref{eq:order_convg}.
\item Using the Trapezoidal and Simpson's methods, compute the energy loss due to GW emission from binary black holes using the numerical-relativity data discussed in Sec.~\ref{sec:BBH_nr_data_fd}. The radiated energy can be computed from the GW polarizations as
