“Transparent" Boundary Conditions for the Equation of Rod Transverse Vibrations

2018. No. 1811.05311.

Гордин В. А., Шемендюк А. А.

Local perturbations of an infinitely long rod go away to infinity. On the contrary, in the case of a finite length of the rod the perturbations reach its boundary and are reflected from them. The boundary conditions constructed here for the implicit difference scheme imitate the Cauchy problem and provide almost no reflection. These boundary conditions are non-local in time, and their practical implementation requires additional calculations at every time step. To minimise them, a special rational approximation similar to the Hermite - Padé approximation is used. Numerical experiments confirm the high "transparency" of these boundary conditions.

Ключевые слова: rational approximation, implicit scheme, рациональная аппроксимация, Rod Equation, Boundary Condition, Finite-Difference Approximation, Z-transformation, Уравнение колебаний стержня, Граничное условие, конечно-разностная аппроксимация, Неявная схема, Z-преобразование

ПУБЛИКАЦИЯ ПОДГОТОВЛЕНА ПО РЕЗУЛЬТАТАМ ПРОЕКТА: Математические модели. Дифференциальные уравнения и большие массивы информации. Аналитические и вычислительные методы. Практические приложения (2018)