On a family of finite-difference schemes with discrete transparent boundary conditions for a parabolic equation on the half-axis
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| Format: | Preprint |
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2012
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| _version_ | 1866917178628898816 |
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| author | Zlotnik, Alexander Koltsova, Natalya |
| author_facet | Zlotnik, Alexander Koltsova, Natalya |
| contents | An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averagings both in time and space. Stability in two norms is proved by the energy method. Also discrete transparent boundary conditions are rigorously derived for schemes by applying the method of reproducing functions. Results of numerical experiments are included as well. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1211_3613 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | On a family of finite-difference schemes with discrete transparent boundary conditions for a parabolic equation on the half-axis Zlotnik, Alexander Koltsova, Natalya Numerical Analysis 65M06, 65M12 An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averagings both in time and space. Stability in two norms is proved by the energy method. Also discrete transparent boundary conditions are rigorously derived for schemes by applying the method of reproducing functions. Results of numerical experiments are included as well. |
| title | On a family of finite-difference schemes with discrete transparent boundary conditions for a parabolic equation on the half-axis |
| topic | Numerical Analysis 65M06, 65M12 |
| url | https://arxiv.org/abs/1211.3613 |