The algorithm of Fredholm first kind integral equation solution which are used in electro-optics and dynamic light scattering is considered. The presented algorithm, unlike other algorithms aimed at solving the same problem, uses the peculiarities of the kernels of integral equations by applying additional constraints to the solution using specifically constructed penalty functions. This makes the precision of the solution higher for functions of one argument and allows to reliably solve integral equations with the solution as a function of two arguments.