I know that the eigenvalue problem for the homogeneous Fredholm integral equation of the 2nd kind:
$$\phi(x) = \lambda \int_a^b K(x, t) \phi(t) dt$$
can be reduced to a matrix eigenvalue problem given as:
$$\phi = \lambda A \phi$$
where $\phi$ is a discretized version of the function $\phi(x)$ and $A$ is the matrix that represents the operator $\mathcal{L(\cdot)}=\int_a^bK(x, t)(\cdot)dt$ . An example method to solve the integral equation is the Nystorm method.
My question is about integral equations in higher dimensions, like two for example. Is there an equivalent matrix formulation of the following integral equation:
$$\phi(x,t)= \lambda \int_a^b \int_c^d K(x, t;y,s)\phi(y, s) dy ds$$