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A Numerical Solution to the Two-Dimensional Nonlinear Degenerate Heat Conduction Equation with a Source

Авторы: Kazakov A.L., Spevak L.F., Nefedova O.A.

Журнал: AIP Conference Proceedings: 14th Intern. Conf. on Mechanics, Resource and Diagnostics of Materials and Structures (MRDMS 2020; Ekaterinburg; 9-13 November 2020)

Том: 2315


Год: 2020

Отчётный год: 2020


Местоположение издательства:


Аннотация: The paper develops an algorithm for solving the two-dimensional nonlinear degenerate parabolic heat conduction equation with a source depending on required function, with a specified law of heat wave front motion. The algorithm based on the boundary element method is implemented in the form of a program. To verify it, we use exact solutions the construction of which is reducible to solving a Cauchy problem for ordinary differential equations with a singularity before the highest derivative. The solutions to the Cauchy problem are constructed in the form of power series with recurrently computed coefficients (with a proof of the statement providing its convergence) and by the boundary element method.

Индексируется WOS: 1

Индексируется Scopus: 1

Индексируется РИНЦ: 1

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