An approach to the construction of regularizing algorithms is considered in the problem of finding a stable approximate solution of the operator equation $Au=f$, where $A$ is a continuous operator from $C[a,b]$ to a normed linear space $F$, when there are a priori restrictions on the exact solution $u(x)$. The method is numerically implemented for the solution of Volterra integral equations and Fredholm integral equations of the first kind, when there is a priori information of various types. The algorithm is realized in the form of a program for IBM PC AT. In the finite-dimensional approximation the irregular grids for the right-hand side, the kernel and the desired solution of the equation are used. Such grids are useful in application of the algorithm to specific practical problems.