This paper investigates the jointly power allocation, flow and congestion control problem in the limited powered wireless multi-hop networks with the previously-established routes, and designs an efficient second-order algorithm based on the primal dual interior point method. The proposed algorithm utilizes the matrix splitting technology to realize distributed update of source rate and node power, and ultimately, optimizes the network utility. The simulation results show that the proposed algorithm significantly reduces the power consumption and improves the energy efficiency, furthermore, it has fast and reliable convergence performance compared with the traditional Lagrange primal-dual approach.