Making network solvers globally convergent

Stationary network problems are considered, unifying linear Kirchhoff equations and non-linear element equations, possessing a proper signature of the derivatives. The global non-degeneracy of the Jacobi matrix is proven, providing the applicability of globally convergent tracing algorithms for such systems. It is shown that stationary problems in gas transport networks can be written in the form necessary for the global convergence. Two stabilized algorithms for the solution of these problems are implemented. The algorithms outperform a standard Newtonian solver for a number of realistic networks. The algorithms do not depend on the staring point, are stable, converge for all scenarios and, additionally, provide feasibility indicator for the problem statement.