Numerical-analytical method for solving initial-boundary value problem for loaded parabolic equation - Assanova, A.T.; Kadirbayeva, Zh.M.; Kuanysh, S.K. (Karagandy University of the name of acad. E.A. Buketov, 2025)
An initial-boundary value problem for a loaded parabolic equation in a rectangular domain was considered. By discretization with respect to a spatial variable, the problem under study is reduced to the initial problem for a system of loaded ordinary differential equations. Based on the previously obtained results of Dzhumabaev and Assanova, an estimate for the solution of the original initial-boundary value problem for a loaded parabolic equation was established. An auxiliary initial problem for a system of loaded ordinary differential equations is solved by the Dzhumabaev parameterization method. Conditions of the unique solvability of the considering problem are obtained and algorithms for finding a solution are constructed. The results are illustrated with a numerical example.
Keywords: 2020 Mathematics Subject Classification; numerical solution; polygonal method; parameterization method; solvability conditions; initial-boundary value problem; loaded parabolic equations; 35К20; 34К10; 65М22; 35R10