[en] To predict the thermal-hydraulic transients, an analytical method has been developed for single and two-phase flow in arbitrary piping networks. In this method the piping network is represented by vessels and flow channels. The thermal-hydraulic transients in the channel are described by partial differential equations derived from mass, momentum and energy conservation laws. The partial differential equations are solved implicitly, simultaneously for the whole network, with the ordinary differential equations that describe the change of vessel pressures and enthalpies. Numerical calculation error is evaluated in the implicit method for the integration of partial differential equations of channel flow. In the numerical calculation an artificial diffusion appears with a diffusion coefficient δtlambda₂/2, where δt is a time step and lambda denotes the propagation velocity of the perturbation. (orig.)