536.2 Method of additional boundary conditions in boundary value problems of thermal conductivity

Trubitsyn K. V. (Самарский государственный технический университет)

BOUNDARY VALUE PROBLEM, EXACT SOLUTION, ADDITIONAL BOUNDARY INFORMATION, LEAST SQUARES METHOD


doi: 10.18698/2309-3684-2025-2-6881


A method has been developed for obtaining exact analytical solutions to boundary value problems of mathematical physics, based on determining additional boundary information that allows the original differential equation to satisfy the required solution at boundary points. Execution of the equation on the boundaries leads to its execution inside the region under consideration, excluding its direct integration over the spatial variable. The eigenvalues are found from the solution of a time ordinary differential equation with respect to an additional function defined at one of the boundary points. Note that in classical methods for obtaining exact analytical solutions, the eigenvalues are found from the Sturm-Liouville boundary value problem defined in the domain of spatial coordinates. Consequently, in this work we consider another direction in determining eigenvalues that coincide with their exact values. The integration constants of an ordinary differential equation with respect to an additional function are found from the initial condition using the least squares method, which makes it possible to eliminate the determination of complex integrals over a spatial variable.


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