Abstract: Mathematical models of the mainline and branches of complex branch-like pipeline network system are nonlinear partial differential equation systems. In some cases, the equation systems can be linearrized, and then be solved with analytical methods. The simultaneous mathematical model is a Volterra integral equation system of the first kind based on the relation connection conditions between the mainline and the branches. Usually the solution of integral equation of the first kind is not stationary, it must be solved with particular methods.Therefore,the method in this paper is proved reliable and practicable.

Key words: Complex Branch-like Pipeline Network, Volterra Integral Equation System, Ill-posed Problem, Regularization Method