A method for approximating the solutions of the kinetic coagulation equation by generalized functions (GA method) is described. The method allows a proper description of the coagulating system integral dynamic behavior using a small number of node points. An algorithm is developed for computing coefficients of the generalized functions and "floating"' nodal point coordinates depending on time. Comparison with asymptotic integral value behavior laws following from self-similarity considerations validates the GA method and confirms its high accuracy tip to very long dimensionless times of the process.