2
$\begingroup$

I want to use Simpson's rule to evaluate the following double integral: $$\int_{a}^{b}\left|\int_{0}^{z}x\cdot \mathrm{erf}(x-10)\cdot J_{0}(x) \mathrm{dx}\right|^{2}\exp(-0.5*(z-40)^2)\mathrm{dz} $$

Usually, if both the limits were numeric I would get away with just applying simps from scipy.integrate twice, but here I have no idea how to proceed.

$\endgroup$
4
$\begingroup$

Your integral can be written as $$ \int_a^b f(z)^2 h(z) dz \approx \sum_q f(z_q)^2 h(z_q) w_q $$ where I wrote some quadrature approximation. Now do another quadrature for $f(z)$ $$ f(z) = \int_0^z g(x) dx \approx \sum_q g(x_q) v_q $$ where $x_q \in [0,z]$ are some quadrature nodes and $v_q$ are corresponding weights.

Write a function to compute $f(z)$ that does the second quadrature. Then use that do the first quadrature.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.