# Questions tagged [integral-equations]

Questions which deal with or solve for functions expressed in integral form, i.e., one or more unknown functions that appear under an integral sign.

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### Find area between three curves

I am trying to find the area between these three curves y=6/x, y=x+4 and y=x-4. Is there any good command to use in mathematica to make it simple?
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### How can I change the dependent variables of a function?

What I want is to define a function which depends of some variables and then get the expression for that same function when it depends of different variables. My specific case is: (where ...
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### Integrate real function returns complex function [closed]

I want to compute the integral $$\int_0^c \exp(-cx+x^2) \mathrm{d}x,$$ where $c>0$ is an unknown constant. In Mathematica Version 12.2.0 ...
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### Not able to reproduce the result of this paper to test if a system is chaotic or nonchaotic

I am trying to reproduce the results of a paper A new test for chaos in deterministic systems by Georg A. Gottwald and Ian Melbourne. This paper talks of a simple 1-0 method to determine whether a ...
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### Evaluating expected improvement in Mathematica

There is a concept in optimization called expected improvement where you sequentially search for the value of x that optimizes the problem. Here is a screen shot of the general idea of the derivation: ...
244 views

### NDSolve cannot solve an ODE system with functions given as integrals-

The problem is that my Mathematica programme cannot solve the differential algebraic equations system. To simplify the problem as much as possible I will consider only the differential equation (which ...
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### Solving the Lotka-McKendrick model with NDSolve

The Lotka-McKendrick model is a demographic model that represents the way a population changes over time due to fertility and mortality. For an age-specific population density $u(a, t)$, and a total ...
239 views

### Solving partial integro-differential equation

I want to solve a partial integro-differential equation of this form: using NDSolve, something like ...
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### NDsolve Boundary Condition is a Function of the Solution

I am trying to solve something like Fick's Law using NDSolve: $$\frac{\partial \varphi}{\partial t}=\frac{\partial^2 \varphi}{\partial r^2}+F(r,t)$$ Subject to a ...
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### Numerically solving an ODE whose right-hand side involves an integral

In a 1955 paper on surfaces of constant negative Gaussian curvature, Marc-Henri Amsler defines a function $w(x)$ by giving the ordinary differential equation $$w'(x)=\frac{1}{x}\int_0^x \sin(w(t))dt,$$...
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### Solving integro-differential equation [closed]

I would like to solve the integro-differential equation of the form $$\left( -n \int_0^b b db + \frac{i \Lambda l_P^2}{9V_c}\frac{d}{db}+b^2+k\right)\psi(b)=0.$$ I followed the steps in Solve an ...
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### How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?

I'm trying to find the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$ where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
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### Getting two different results for the same computation

I have the following two codes: ...
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### Gaussian Integral incorrect

I'm trying to learn about the Gaussian Normal distribution using Mathematica. So I defined my Gaussian like this ...