# 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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### What are the differences between these different forms of equation?

What are the differences between Conservative differential form, Non-conservative differential form, Conservative Integral form and Non-conservative integral form of differential equations? I know ...
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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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### 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 $e_{q}=2[1-cos(2\pi q)]$ ...
### 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 ...
I'm looking for an algorithm for solving numerically, for u(t) and v(t), the following system: $$u(t)=u_{0}-ct+\int_{0}^{t}\frac{a}{1+b_{1}e^{u(s)}+b_{2}e^{v(s)}}ds$$  v(t)=v_{0}-Ct+\frac{CT}{\...