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Numerical study of travelling wave type solutions for the nonlinear heat equation

Авторы: Kazakov A.L., Spevak L.F.

Журнал: AIP Conference Proceedings: Proc. of the 13th Intern. Conf. on Mechanics, Resource and Diagnostics of Materials and Structures (MRDMS'2019)

Том: 2176


Год: 2019

Отчётный год: 2020


Местоположение издательства:


Аннотация: The problem of constructing solutions to the nonlinear heat equation with power nonlinearity is considered. The solutions have the form of a traveling wave and simulate the propagation of disturbances over a cold background with a finite velocity. It is shown that the construction can be reduced to the Cauchy problem for an ordinary second-order differential equation with a singularity multiplying the highest derivative. Its solutions are constructed using the boundary element method based on the dual reciprocity method. A computational experiment is carried out. The results are compared with the solutions of the same problems by the power series method. The calculations have shown the correctness of the developed boundary element algorithm and its advantage compared to the power series segments and the step-by-step method previously proposed by the authors.

Индексируется WOS: 1

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