Tagged Questions
5
votes
1answer
78 views
Method selection for numeric quadrature
Several families of methods exist for numeric quadrature. If I have a specific class of integrands how do I select the ideal method?
What are the relevant questions to ask both about the integrand ...
11
votes
3answers
165 views
Numeric Quadrature with Derivatives
Most numerical methods for quadrature treat the integrand as a black-box function. What if we have more information? In particular, what benefit, if any, can we derive from knowing the first few ...
13
votes
1answer
144 views
Does transforming $J_0(x)\to\int\cos(x\sin\theta)$ help with numerical integration?
I've heard anecdotally that when one is trying to numerically do an integral of the form
$$\int_0^\infty f(x) J_0(x)\,\mathrm{d}x$$
with $f(x)$ smooth and well-behaved (e.g. not itself highly ...
10
votes
2answers
237 views
Numerical Integration - handling NaNs (C / Fortran)
I am dealing with a tricky integral that exhibits NaNs at certain values near zero and at the moment I am dealing with them quite crudely using an ISNAN statement which sets the integrand to zero when ...
9
votes
3answers
329 views
Numeric integration of multi-dimensional integral with known boundaries
I have a (2-dimensional) improper integral
$$I=\int_A \frac{W(x,y)}{F(x,y)}\,\mbox{d}x\mbox{d}y$$
where the domain of integration $A$ is smaller than $x=[-1,1]$, $y=[-1,1]$ but further restricted by ...
12
votes
5answers
442 views
How can I approximate an improper integral?
I have a function $f(x,y,z)$ such that
$\int_{R^3} f(x,y,z)dV$
is finite, and I want to approximate this integral.
I'm familiar with quadrature rules and monte carlo approximations of integrals, ...
7
votes
3answers
176 views
Numerical integration of compactly supported function on a triangle
as the title suggests I'm trying to compute the integral of a compactly supported function (Wendland's quintic polynomial) on a triangle. Notice, that the center of the function is somewhere in 3-D ...
2
votes
1answer
404 views
Error calculation in trapezoidal rule
If we use the composite trapezoidal rule, then what is the least number of divisions $N$ for which the error of the integral $\int^1_0{e^{-x}}dx$ doesn't exceed $\frac{1}{12}\times10^{-2}$.
My guess ...
5
votes
0answers
93 views
Suggestions for numerical integral over Pólya Distribution
This problem arises from a Bayesian statistical modeling project. In order to compute with my model, I need to perform an integration in which part of the integrand is the "Pólya" or ...
6
votes
1answer
216 views
What numerical quadrature to choose to integrate a function with singularities?
For example, I would like to numerically compute the $L^2$-norm of $\displaystyle u = \frac{1}{(x^2+y^2+z^2)^{1/3}}$ in some domain that includes zero, I tried Gauss quadrature and it fails, it is ...
5
votes
2answers
271 views
numerical integration with possible division by 'zero'
I am trying to integrate
$$\int^1_0 t^{2n+2}\exp\left({\frac{\alpha r_0}{t}}\right)dt$$
which is a simple transformation of
$$\int^{\infty}_1 x^{2n}\exp(-\alpha r_0 x)dx$$
using $t = \frac1{x}$ ...
15
votes
3answers
506 views
What's the state-of-the-art in highly oscillatory integral computation?
What's the state-of-the-art in the approximation of highly oscillatory integrals in both one dimension and higher dimensions to arbitrary precision?
