Numerical modeling of wave processes on a graph

Title	Numerical modeling of wave processes on a graph
Authors	M. A. Rybakov¹ ¹Derzhavin Tambov State University
Annotation	The investigation of vibrations in elastic string networks is crucial for the analysis of vibroacoustic properties of civil and aerospace structures, the prediction of resonant behavior, and the design of vibration isolation systems. The present work considers an initial-boundary value problem for the wave equation on a graph that describes such vibrations. The coupling conditions at the graph nodes enforce continuity of displacement and force balance, thereby accounting for both ideal joints and joints where external influences and stiffness changes of adjacent strings (graph edges) decelerate or accelerate the wave propagation. An explicit finite-difference scheme with double nodes is used for the numerical solution. Numerical experiments have verified the stability and accuracy of the proposed method.
Keywords	numerical modeling, initial-boundary value problem, wave process, graph, coupling conditions.
Citation	Rybakov M. A. ''Numerical modeling of wave processes on a graph'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 189-192. Available at: https://conf.svmo.ru/files/2026/papers/paper102.pdf. - Date of access: 25.09.2026.