# Questions tagged [integral-equations]

Questions regarding the numerical solution and analysis of equations that feature an integral transform on the unknown function. Problems with integral-equation formulations, their discretization, calculation and usage of Green's functions, eigenvalue analysis of the integral operators, and software recommendations should be marked with this tag.

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### Huygens Fresnel Diffraction integral using dblquad in python

I am attempting to create a python function to assist in calculating the following numerical integration of the Huygens Fresnel integral in the form of ...
1 vote
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### Finite difference solver for the 2D Poisson's equation with an integral boundary condition

I wanted to attempt an implementation of a finite-difference-based solver for the 2D elctrostatic Poisson equation when metallic objects are present. Also, I hope to take as input, the location of ...
30 views

### Using Pymc3+Theano+astropy for Bayesian inference with integral expressions

This is my first time using Pymc3 or Theano, so I apologize if this question is straightforward. I'm interested in using Bayesian inference to see how effective the (non) observation of something can ...
1 vote
135 views

### Efficient multidimensional numerical integration in R and C++

I'm trying to perform a 4-dimensional numerical integration in R using a function I wrote in C++ code which is then sourced in <...
46 views

750 views

### Unstructured mesh vs hybrid structured/unstructured for numerical simulations

While answering one of the questions on meshing process, I encountered a lack of understanding on my end for the comparison of the mesh quality. First, consider an unstructured mesh created in GMSH ...
773 views

339 views

### Numerical integration of given points, simple/easy way

I have the x and the f(x) for a set of x. I don't know the function, actually. This is ...
843 views

### Solve integral equation for unknown constant

Consider the equations $$\int_0^L \mathbf W(\mathbf u, s) \, \mathrm ds = \mathbf 0$$ where $0 \leq s \leq L$ and $\mathbf u$ is a vector of constants. Numerically, what is the best way to ...
185 views

1 vote
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9k views

### Applying the Runge-Kutta method to second order ODEs

How can I replace the Euler method by Runge-Kutta 4th order to determine the free fall motion in not constant gravitional magnitude (eg. free fall from 10 000 km above ground)? So far I wrote simple ...
342 views

### Mathematica NIntegrate function in C++

I am working on computing a challenging integral. I am working with someone else who wrote some code in Mathematica to compute it. I do not have mathematica so I am trying to do the same thing in C++. ...
82 views

### Solving condensate density problem in MATLAB

I want to solve for $n_{0}$ for a fixed value of $n$, lets say $n=1$ $$n= n_{0}+ \dfrac{1}{2}\int_{-1/2}^{1/2}dq\left(\dfrac{e_{q}+Un_{0}}{\hbar\omega}-1\right)$$ where $e_{q}=2[1-cos(2\pi q)]$ ...
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### How to integrate Euler Bending Equation in C++? [closed]

I am trying to Draw shear force diagram and bending moment diagram of beams. In this, I need to integrate second order differential. So, Anybody can suggest me, which numerical method should I use?
151 views

### Computing expectations

I want to compute the following conditional expectation $E_{t}[\phi(A_{t+1}, \eta_{t+1})| A_t]$ where $\log A_{t}=\rho \log A_{t-1} + e_{t}$ and $e_{t}$ is IID $N~(0,\sigma_e)$ and $\eta_{t}$ is ...
629 views

### Can the conservative form of the advection equation be re-written by replacing the velocity term with an integral over all other points in space?

Suppose I have a 1D advection equation in conservation (divergence) form $\partial_t u(x,t) = -\partial_x [v(x)u(x,t)],$ where $u$ is a conserved quantity in space, and $v$ gives the velocity of the ...
1 vote
98 views

### Package for integration over non-rectangular region

I want to compute the expected value of a multivariate function f(x) wrt to dirichlet distribution. My problem is "penta-nomial" (i.e 5 variables) so calculating ...
1 vote
282 views

### Solve a fourth order differential equation

I want to solve $$\frac{\partial^2}{\partial t^2}u(z,t) + a\frac{\partial^2}{\partial z^2}u(z,t) + k\frac{\partial^4}{\partial z^4}u(z,t) = 0$$ with $u(z,0) = 1+0.1e^{-\frac{z^2}{2}}$. I'd like to ...
273 views

### Solve a differential equation with finite difference method

I want to solve this equation $$-\frac{1}{2}f''(x)+2a\ f(x)^3 = f(x)\mu$$ One exact solution (there are a lot of different kinds) of this equation is $f(x) = f_\infty \tanh(\sqrt{2a}f_\infty x)$ (...
2k views

### Line Integral Convolution (LIC) Requirements

I'm trying to plot some vector fields using LIC technique. More specifically, I'm using the Python solution for this kind of plot. Before applying that approach, I was plotting my vectors as quiver. ...
189 views

### Integration of nonlinear PIDE via spectral methods

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction \$\...
383 views

### Periodic Green's functions in integral equation methods in different frequency regimes

I'm asking about the solution of the Helmholtz equation on a periodic domain with piecewise constant wavespeed in different frequency regimes. One possible approach is to solving this problem is to ...
818 views

### Matlab: Error in integral function

I want to compute an integral with the following code written in Matlab. ...
I have a nasty system of coupled integral equations, which I managed to discretize and recast a non-linear system, i.e. something like: $$\vec{w} = F \left( \vec{w} \right) \hspace{32pt} w \in \... 3 votes 1 answer 412 views ### Finite difference equations versus boundary integral equations for elliptic pdes In certain cases, boundary integral methods are preferred for elliptic partial differential equations as opposed to finite difference methods. For instance, for solving the Poisson equation in a ... 3 votes 0 answers 92 views ### analytic or numeric integral of diverging function I'm trying to carry out the following integral numerically$$\int_{r_\mathrm{in}}^{r_\mathrm{out}} \Sigma\left(r'\right) \frac{r'}{r} \left( \frac{1}{r-r'}\, E(L) + \frac{1}{r+r'}\, K(L) \right) \... 