This paper aims to analyse the stability of a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks composed of agents with first-order dynamics. In particular, in the analysed class a single evaluation of a nonlinear function of the consensus error is performed per each node. The classical assumption of switching among connected graphs is dropped here, allowing to represent failures and intermittency in the communications between agents. Thus, conditions to guarantee finite and fixed-time convergence, even while switching among disconnected graphs, are provided. Moreover, the algorithms of the considered class are computationally simpler than previously proposed finite-time consensus algorithms for dynamic networks, which is an essential feature in scenarios with computationally limited nodes and energy efficiency requirements such as in sensor networks. Simulations illustrate the performance of the proposed consensus algorithms. In the presented scenarios, results show that the settling time of the considered algorithms grows slower than other consensus algorithms for dynamic networks as the number of nodes increases.