# 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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### Solving a Volterra integral equation

I review this question Solving a Volterra integral equation numerically. But I can not understand that. I have the following code: ...
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### NIntegrate::inumr Error For Multiple NIntegrate Operations

I would like some help trying to use Mathematica (I just started using it!) to compute the numerical integration of a complicated function (assigned "longitudinalWake" in this example). Essentially, I ...
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### Nested Integrals Using NIntegrate Not Converging

I have a mathematica script/code that I wrote that involves a few nested NIntegrate functions but its not converging. I let it run for about a week before calling it quits. I am a beginner with ...
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### How to solve the integro differential equations with matrix

I have integro-differential equations like $X'(t)=\operatorname{diag}(\int_0^t X(t) dt)AX(t)-X(t)$, where $A$ is a known $N\times N$ matrix and $X$ is a $N\times 1$ vector, and $\operatorname{diag}$...
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### exponential differential integral equation

I have a following equation, which has a singular kernel, ...
153 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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### How to solve a system of integral equations [closed]

I am trying to solve a system of equations as follows... f1[t]/3 == (1/3)[Integrate[f3[t], t]] f1[t]/(6/5) == Integrate[f2[t], t] f3[t] == Integrate[f1[t], t] I ...
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### Integral equation solving

So there is this equation that I have to numerically solve for T: Q/(3nRT) = f(T/300) - f(T/77) Here Q = 920.364, n = 0.24, R = 8.314 while f is defined as the ...
292 views

### How do I solve a nonlinear Fredholm integral equation?

$u(x)= 1/3+\int_{0}^{1}x\,t\sqrt{u(t)}\,dt$ u[x] == 1/3 + Integrate[x t Sqrt[u[t]], {t, 0, 1}] Any ideas on how to treat such a problem with Mathematica ...
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### Solving PDE involving Hilbert transform numerically

I'm trying to solve the following equation numerically: $$u_{tt}-\mathcal{H}(u_x)=A^2_{xx},$$ where $\mathcal{H}$ is the Hilbert transform and $A$ is a prescribed forcing function which we assume ...
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### Solving Fredholm equation of the 2nd kind

While I was using the code from here to solve this integral equation: ...
122 views