# 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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### It is possible to solve integro-differential equations using in Fenics?

I am interested in solve the following integro-differential equation: \begin{align} \frac{\partial{\rho(\theta, t)}}{\partial{t}} = D \frac{\partial{\rho(\theta, t)}}{\partial{\theta^2}} - \beta \...
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### Solve integral $\int_{-\infty}^{\infty} e^{-x^2}dx$

i trying to solve this integral $$\int_{-\infty}^{\infty} e^{-x^2}dx$$ I'm using this CODE ...
1 vote
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### Gauss Integration of $\sqrt(x)$

I want to construct a gauss integration for the weight function $w(x) = x^{1/2}$ for $$\int_{0}^{1}x^{1/2}f(x)dx = a_{1}f(x_{1})+a_{2}f(x_{2})$$ Solving \begin{align*} a_{1}+a_{2} =& \int_{0}^{...
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### Book recommendation on numerical methods for solving Integro-Differential equations

I was wondering if anyone could recommend a good book or resource on numerical methods for solving integro-differential equations? Of course I am familiar with the methods for solving ODEs and PDEs ...
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### A Question About a Claim from 1991 Computational EM paper about the Cancellation of certain Boundary Terms

Please let me know if this is not the appropriate site for this question. I found questions regarding EFIE/MFIE/CFIE on this site, so I thought my question might fit. I am studying the paper by Putnam ...
1 vote
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### Convolution in Python

I have an integral of a convolution between two functions. How can I calculate this in Python? It is a continuum convolution.
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### Best ways to avoid singularities in kernels when solving integral equations numerically

Take a Fredholm integral equation $$u(x) - \lambda \int_{-1}^{1} K(x,y)u(y) \, \mathrm{d} y = f(x)$$ and discretize it via (say) Gaussian quadrature with nodes $\{x_j\}$ and weights $\{w_j\}$ to get ...
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### Calculation of the EFIE integral

I need help computing the following integral: $$\int_{}\frac{(1+jk|\vec{r}-\vec{r}^\prime|)e^{-jk|\vec{r}-\vec{r}^\prime|}}{|\vec{r}-\vec{r}^\prime|}d\vec{r}^\prime$$ in this integral $\vec{r}$ ...
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### Stability of different quadrature rules in 1st-kind Volterra integral equation

I am dealing with a integral equation $$f'(t) = -\int_0^t K(s) f(t-s)\quad t\in [0,t_\max] \tag{1}$$ in which $f(t)$ and $f'(t)$ are known, well-behaved functions of $t$ and $K(t)$ is the unknown. In ...
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### Complex Integral Equation Solution in MATLAB

I need to solve an integral equation in the form: $$A(z)+\int\limits^{z_2}_{z_1}B(z') \frac{z^N}{z^N-z'^N} \frac{e^{i\beta}}{|z|}\mathrm{d}z'=0$$ where $A(z)$ distribution is known and we are ...
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### Computing dilogarithm

I'm measuring the integral of a quantity which, mathematically, requires the computation of a dilogarithm function. $$\operatorname{Li}_2(be^{ax})$$ where $b$ and $a$ (are real and) can be positive ...
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### Broadening spectral data by using FFT's

I obtain numerical discrete data of the form $$S_{raw}(\omega) = \sum_{j}w_{j} \delta(\omega-\omega_{j})$$ to compare the result with experimental data the delta peaks need to be broadened ...
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### Quick scheme for separable first-order ODE

I'm trying to integrate an incredibly simple ODE: $$y'(x) = -f(y),\quad y(0) = y_0 \ ,$$ from $x=0$ to $x=1$. This is a decay type of equation, $f$ is the (variable) decay rate and $y$ is the ...
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### Integration including bessel function

I’m trying to evaluate an improper integral of a 0th order Bessel function of the first kind using Matlab: v = integral(@(x)besselj(0, x), 0, Inf) which returns ...
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