Questions tagged [integro-differential-equations]

An integro-differential equation is an equation involving both the integrals and derivatives of a function. The solution to an integro-differential equation is a function which satisfies the original equation.

An integro-differential equation is an equation involving both the integrals and derivatives of a function.

Solution methods include differentiating to obtain a purely differential equation and transform methods such as the Laplace Transform.

Integro-differential equations appear in applications such as RLC linear circuits, when finding the current.

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From the Radiative Transfer Equation to the "Volume Rendering Equation". Derivation

I am studying computer graphics and have read several references in this field on the topic of volume rendering/rendering participating medium. They generally start from the Radiative Transfer Equation which I know is provided in S. Chandrasekhar's…
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I need to solve an integral equation with feedback

I've encountered the following equation: $p_t = \pi_t + c \int_{-\infty}^te^{-\gamma(t-\tau)}dp_\tau, \quad 0<\gamma, 0
Mik92
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How can I find an analytical solution for this integro-differential equation?

I want to find analytical solutions of the following integro-differential equation: $\left(A\nabla_{\rho}^2 + B\nabla_z^2\right)f(\vec{r}) = C \int{ g(\vec{r},\vec{r\,'}) f(\vec{r\,'})d\vec{r\,'}}, \qquad g(\vec{r},\vec{r\,'}) =…
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Survival probability integro-differential equation question

For the Classical Risk model, the survival probability, $\phi(u)$, satisfies the integro-differential equation: $$\phi(u)=1-\psi(u)=\int\limits_o^\infty \int\limits_o^{u+ct}\lambda e^{-\lambda t}\phi(u+ct-x)f_X(x)dxdt.$$ Where $\psi(u)$ is the ruin…
Amber
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Solving a volterra integro-differential equation

I've encountered a problem where I have to solve a volterra integro-differential equation of the following format. I tried different approaches but the exponential term makes the life miserable. Any suggestions? $-u'(t) = a^2\int_0^tdx u(x)…
Sachin
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