Discrete transparent boundary conditions for the equation of rod transverse vibrations |
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| Affiliation: | 1. National Research University Higher School of Economics, Moscow, Russia;2. Hydrometeorological Centre of Russia, Moscow 123242, Russia;1. Department of Mathematics, Faculty of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia;2. Department of Basic Engineering Science, Faculty of Engineering, Menofia University, Shebin El-Kom 32511, Egypt;3. Department of Mathematics, College of Science and Humanities at Howtat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia;4. Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box 741, Tabuk 71491, Saudi Arabia;5. Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, Porto 4249-015, Portugal;1. Institute of Petroleum Geology and Geophysics SB RAS, 3 Koptug ave., Novosibirsk 630090, Russia;2. Sobolev Institute of Mathematics SB RAS, 4 Koptug ave., Novosibirsk 630090, Russia;3. Novosibirsk State University, 2 Pirogova st., Novosibirsk 630090, Russia;4. Mathematical Center in Akademgorodok, 2 Pirogova st. & 4 Koptug ave., Novosibirsk 630090, Russia;1. Department of Mathematics, Shaheed Bhagat Singh College, University of Delhi, India;2. Government P.G. College, Mushafirkhana, Uttar Pradesh, India;1. Department of Basic and Applied Sciences, Punjabi University, Patiala, Punjab, India;2. Kurukshetra University Kurukshetra, India;1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 200016, China;2. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;3. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China |
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| Abstract: | Local perturbations of an infinitely long rod travel to infinity. On the contrary, in the case of a finite length of the rod, the perturbations reach its boundary and are reflected. 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 with respect to 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 and determine the conditional stability regions for finite-difference scheme. |
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