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Given the following system of linear integro-differential equations

$$ \frac{d}{d t}B(t)+\int_{0}^{+\infty}C(x,t)dx+A(t)=0,\\ \left[\frac{\partial}{\partial t}+V(x)\right]C(x,t)+B(t)=0,\\ \frac{d}{d t}A(t)+B(t)+I_{0}=0, $$

with initial conditions $A(0)=0,B(0)=0,C(x,0)=0$, where $V(x)=1/x$ and $I_{0}=1$.

How to numerically compute a solution of $A(t)$, $B(t)$, and $C(x,t)$ for above system of equations in Matlab ?

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