# Tagged Questions

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 ...
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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 ...
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### 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 ...
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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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 ...
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### 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 "PĆ³lya" or ...
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### 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 ...
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 $t = \frac1{x}$ ...