# Tagged Questions

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### Are there methods to solve coupled integral and integro-differential equations?

I have one fredholm integral equation $$y(x)=f(x)+\int_0^1 K_1(x,g(x),t)y(x(t))dt$$ and an integro-differential equation $$\frac{dg(x)}{dx}=h(x)+\int_0^1 K_2(x,y(x),t)g(x(t))dt$$. Are there any ...
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### numerical implementation of the resolvent kernel of an integral equation

I started exploring implentation of Volterra equations only recently. The iterative kernel for my problem looks like this: $$L_i(x,y) = \int\limits_x^y L_1(y,t)L_{i-1}(t, x)dt.$$ I have been trying ...
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Consider the equation $$g(t) = \int_a^b K(t,s)f(s) ds$$ where $g$ and the kernel $K$ are known and $f$ is to be determined. Suppose that the equation has a solution. Under what conditions on the ...
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### What kind of numerical methods are best applicable to this?

I'm wondering: what would be the best numerical method for solving a nonlinear integral equation of the form $$f(x) = a(x) + \int_{-A}^{A} K(x, t, f(t)) dt$$ where $f$ is the unknown function, a ...
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### How to solve Volterra's integral equation of second kind with numerical solution

The problem occurs to me when I tried to solve \begin{align}E(x)=1+2(1-x)^2\int_{x}^{1}(1-t)E\left(\frac{x}{t}\right)dt\end{align} with $E(1)=1$ and $\lim_{x\to 0^+}E(x) \to +\infty$. I'd like to ...