# Questions tagged [integration]

For questions related to integration on computers. This can include numerical approximations of integrals (e.g. Monte Carlo, quadrature, FEM, RK4) and algorithms/software to obtain analytical derivatives (Risch algorithm, SymPy).

162 questions
Filter by
Sorted by
Tagged with
226 views

70 views

### Importance Sampling for multidimensional integrals and random numbers from multivariable pdf's

I am aiming to get a numerical value for a five-dimensional integral using Monte Carlo Integration. I am getting good results using the Mean Value Method, but I would like to try to use Importance ...
86 views

### What is the best method to do a MC Integration of a multidimensional integral where the integration limits depend upon other variables?

What is the best method to do a Monte Carlo Integration of a multidimensional integral where the integration limits depend upon other variables? I am interested in getting a numerical value of a 5 ...
91 views

### Compute 2D numerical double integration with Boost C++ with parameters

I am trying to compute the double Richardson and Wolf integrals for the focusing of a lens with Boost in C++ (using the Gauss Kronrod method). As a starting point, I used the example presented in this ...
29 views

### Sample Average Approximation vs. Numerical Integration

In the sense of the calculation of the expected value of objective functions, we have two choices to evaluate the value; 1. Sample Average Approximation (SAA): $$\frac{1}{N}\sum_{i=1}^N f(x,\xi^i).$$...
908 views

### Error in Simpson's 3/8 rule is higher than that of Simpson's 1/3 rule

For a given function $f(x)$, I have tried to find its numerical integral using Simpson's 1/3 and Simpson's 3/8 rules. I then compare the solution from the numerical quadratures to the analytical ...
47 views

134 views

### Computing infinite series with iterated functions

I found this question (linked here) which asks to find what this infinite series converges to $$\sum_{n=1}^{\infty} \int_0^{\pi} f_n(x) dx$$ where $f_{n+1}(x) = \sin(f_n(x))$ and $f_1 = \sin(x)$. ...
191 views

### Calculating the antiderivative numerically

HeIIo everybody, in the standard literature topics like numerical differentiation and numerical integration are usually discussed in detail. However, numerical integration is not the same as ...