JUCS - Journal of Universal Computer Science 15(6): 1337-1364, doi: 10.3217/jucs-015-06-1337
Computing the Solution Operators of Symmetric Hyperbolic Systems of PDE
expand article infoSvetlana Selivanova, Victor Selivanov
‡ Siberian Division of the Russian Academy of Sciences, Novosibirsk, Russia
Open Access
We study the computability properties of symmetric hyperbolic systems of PDE , with the initial condition = φ(x1,...,xm). Such systems first considered by K.O. Friedrichs can be used to describe a wide variety of physical processes. Using the difference equations approach, we prove computability of the operator that sends (for any fixed computable matrices A, B1, ..., Bm satisfying certain conditions) any initial function φ ∈ Cp+1(Q, ℝn) (satisfying certain conditions), p ≥ 2, to the unique solution u ∈ Cp(H, ℝn), where Q = [0,1]m and H is the nonempty domain of correctness of the system.
hyperbolic system, PDE, computability, metric space, norm, matrix pencil, difference scheme, stability, finite-dimensional approximation