eng
episciences.org
Logical Methods in Computer Science
1860-5974
2017-11-21
Volume 13, Issue 4
10.23638/LMCS-13(4:13)2017
4062
journal article
Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs
Svetlana Selivanova
Victor Selivanov
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.
https://lmcs.episciences.org/4062/pdf
Computer Science - Numerical Analysis
Mathematics - Numerical Analysis
03D78, 58J45, 65M06, 65M25
F.1.1
G.1.8