## 1 Introduction
Each network has its unique particular distribution/transmission characteristics, and changes at a node (supplier or demand) will have consequences throughout the NG transport system [18]. In most countries, gas is distributed by pipeline networks over a vast range of pressures [19]; these are mainly divided into two, high pressure and low pressure systems, which are specified for transmission and distribution lines, respectively. However, in some research simulations, e.g., [18], middle-pressure pipelines are also investigated. Very large users of NG, such as power stations, are supplied directly from the transmission network, while other users including residential users receive NG via the distribution network [20]. A gas network is generally represented by a diagram involving branches (pipelines) and nodes (pipe connections). Facilities and equipment can be divided two groups: active and/or passive [21]. An active node or branch represents a actively-controlled facility, which is controlled during operation, e.g., compressors, regulator valves, and town gate stations. On the other side, the passive equipment will exert an influence on the network; however, its impact is due to the flow conditions, and the device is not adjusted or controlled. The prime example of passive equipment is the pipes [13]. Gas networks are large infrastructures with significant interconnection to the other networks, mainly electrical grids. Therefore, the security of gas supply is important to ensure continuing electricity supply. The challenge in gas networks is to balance the supply from different sources, with the changing demand. By controlling the pressure of the network, the TSO can ensure that sufficient gas is available to supply the end users with sufficient quantities. In this paper, a novel method is used to solve the non-linear system of algebraic equations. It provides a matrix formulation of the non-linear system describing the model, and by using matrix algebra, an alternative linear system is created. The solution of the alternative linear system can be used as a smooth approximation of the solutions of the non-linear system. This formulation is ready for software implementation and may also be used in atomic scale models as an alternative to existing empirical approaches with pair and cohesive potentials. An illustrative example, analysing a local region of a node, is presented to demonstrate the model performance. In this study, two simplified gas networks were created, each based on the Irish Gas Network. Network 1 is A gas network with 13 nodes and 14 pipes, and a bigger network, Network 2, has 109 nodes and 112 pipes. Both networks are used for comparison of the novel approach with numerical solutions. Having a new reliable method for gas network modelling with fast calculation and precise results can be an option to replace numerical solutions, especially for large gas networks, such as those in continental Europe or North America, which contain several hundred nodes and pipelines and where large computation power is required. This new approach is a computational method that helps in producing faster results, and when the modelling of NG networks is coupled with other energy systems, for example the electrical network, faster and less computationally-demanding results are of key importance.