Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs
We discuss possibilities of application of Numerical Analysis methods to proving computability, in the sense of the TTE approach, of solution operators of boundary-value problems for systems of PDEs. We prove computability of the solution operator for a symmetric hyperbolic system with computable re...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2017-11-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/4062/pdf |
| _version_ | 1797268622463205376 |
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| author | Svetlana Selivanova Victor Selivanov |
| author_facet | Svetlana Selivanova Victor Selivanov |
| author_sort | Svetlana Selivanova |
| collection | DOAJ |
| description | We discuss possibilities of application of Numerical Analysis methods to
proving computability, in the sense of the TTE approach, of solution operators
of boundary-value problems for systems of PDEs. We prove computability of the
solution operator for a symmetric hyperbolic system with computable real
coefficients and dissipative boundary conditions, and of the Cauchy problem for
the same system (we also prove computable dependence on the coefficients) in a
cube $Q\subseteq\mathbb R^m$. Such systems describe a wide variety of physical
processes (e.g. elasticity, acoustics, Maxwell equations). Moreover, many
boundary-value problems for the wave equation also can be reduced to this case,
thus we partially answer a question raised in Weihrauch and Zhong (2002).
Compared with most of other existing methods of proving computability for PDEs,
this method does not require existence of explicit solution formulas and is
thus applicable to a broader class of (systems of) equations. |
| first_indexed | 2024-04-25T01:35:24Z |
| format | Article |
| id | doaj.art-4d72aaa884f64d5f861afeb43f8d9393 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:35:24Z |
| publishDate | 2017-11-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-4d72aaa884f64d5f861afeb43f8d93932024-03-08T09:52:12ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742017-11-01Volume 13, Issue 410.23638/LMCS-13(4:13)20174062Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEsSvetlana SelivanovaVictor SelivanovWe discuss possibilities of application of Numerical Analysis methods to proving computability, in the sense of the TTE approach, of solution operators of boundary-value problems for systems of PDEs. We prove computability of the solution operator for a symmetric hyperbolic system with computable real coefficients and dissipative boundary conditions, and of the Cauchy problem for the same system (we also prove computable dependence on the coefficients) in a cube $Q\subseteq\mathbb R^m$. Such systems describe a wide variety of physical processes (e.g. elasticity, acoustics, Maxwell equations). Moreover, many boundary-value problems for the wave equation also can be reduced to this case, thus we partially answer a question raised in Weihrauch and Zhong (2002). Compared with most of other existing methods of proving computability for PDEs, this method does not require existence of explicit solution formulas and is thus applicable to a broader class of (systems of) equations.https://lmcs.episciences.org/4062/pdfcomputer science - numerical analysismathematics - numerical analysis03d78, 58j45, 65m06, 65m25f.1.1g.1.8 |
| spellingShingle | Svetlana Selivanova Victor Selivanov Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs Logical Methods in Computer Science computer science - numerical analysis mathematics - numerical analysis 03d78, 58j45, 65m06, 65m25 f.1.1 g.1.8 |
| title | Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs |
| title_full | Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs |
| title_fullStr | Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs |
| title_full_unstemmed | Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs |
| title_short | Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs |
| title_sort | computing solution operators of boundary value problems for some linear hyperbolic systems of pdes |
| topic | computer science - numerical analysis mathematics - numerical analysis 03d78, 58j45, 65m06, 65m25 f.1.1 g.1.8 |
| url | https://lmcs.episciences.org/4062/pdf |
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