Research output: Contribution to journal › Article › peer-review
Computing solution operators of boundary-value problems for some linear hyperbolic systems of pdes. / Selivanova, Svetlana; Selivanov, Victor.
In: Logical Methods in Computer Science, Vol. 13, No. 4, 13, 2017.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Computing solution operators of boundary-value problems for some linear hyperbolic systems of pdes
AU - Selivanova, Svetlana
AU - Selivanov, Victor
PY - 2017
Y1 - 2017
N2 - We discuss possibilities of application of Numerical Analysis methods to proving computability, in the sense of the TTE approach, of solution operators of boundaryvalue 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 ⊆ ℝm. Such systems describe a wide variety of physical processes (e.g. elasticity, acoustics, Maxwell equations). Moreover, many boundaryvalue problems for the wave equation also can be reduced to this case, thus we partially answer a question raised in [WZ02]. 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.
AB - We discuss possibilities of application of Numerical Analysis methods to proving computability, in the sense of the TTE approach, of solution operators of boundaryvalue 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 ⊆ ℝm. Such systems describe a wide variety of physical processes (e.g. elasticity, acoustics, Maxwell equations). Moreover, many boundaryvalue problems for the wave equation also can be reduced to this case, thus we partially answer a question raised in [WZ02]. 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.
KW - Algebraic real
KW - Boundary-value problem
KW - Cauchy problem
KW - Computability
KW - Constructive field
KW - Difference scheme
KW - Finite-dimensional approximation
KW - Solution operator
KW - Stability
KW - Symmetric hyperbolic system
KW - Systems of PDEs
KW - Wave equation
UR - http://www.scopus.com/inward/record.url?scp=85041855765&partnerID=8YFLogxK
U2 - 10.23638/LMCS-13(4:13)2017
DO - 10.23638/LMCS-13(4:13)2017
M3 - Article
AN - SCOPUS:85041855765
VL - 13
JO - Logical Methods in Computer Science
JF - Logical Methods in Computer Science
SN - 1860-5974
IS - 4
M1 - 13
ER -
ID: 9670792