In article the new numerical method of integration of the ordinary differential equations (ODE) is considered. The method is based on replacement of initial continuous system with equivalent nonsynchronous pulse system. For an estimation of an error of a new method the conclusion of analytical expressions which allow to eliminate a methodical error of numerical formulas of integration (quadrature rules) for known entrance signals is presented. The computer models of a new method realised in tool systems MATLAB/Simulink and LabVIEW/Simulation Module are resulted.