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Numerical-Analytical Treatment of Initial-Boundary Value Problems for Continuum Transport Equations in $n$-Dimensional Network-Structured Domains
| Title | Numerical-Analytical Treatment of Initial-Boundary Value Problems for Continuum Transport Equations in $n$-Dimensional Network-Structured Domains |
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| Authors | V. V. Provotorov1, M. A. Rybakov1 1Northern (Arctic) Federal University named after M.V. Lomonosov |
| Annotation | The paper proposes a numerical-analytical method for solving the initial-boundary value problem for the transport equation of a continuous medium in $n$-dimensional network-like domains. Such problems arise in models of pipeline systems, power grids, building structures, etc. The method uses a finite-differential approximation of derivatives with respect to all variables except one. The boundary value problem for a linear differential-difference system obtained by such an approximation is solved by a symbolic method. The developed approach allows one to obtain approximate solutions in analytical form, which significantly expands the possibilities of applications in various engineering problems. |
| Keywords | network-like domain, initial-boundary value problem, continuous medium transport equation, differential-difference system. |
| Citation | Provotorov V. V., Rybakov M. A. ''Numerical-Analytical Treatment of Initial-Boundary Value Problems for Continuum Transport Equations in $n$-Dimensional Network-Structured Domains'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 225-229. Available at: https://conf.svmo.ru/files/2025/papers/paper45.pdf. - Date of access: 30.08.2025. |
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