Computing the Solution Operators of Symmetric Hyperbolic Systems of PDE

Svetlana Selivanova; Victor Selivanov

doi:10.3217/jucs-015-06-1337

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

Svetlana Selivanova^‡, Victor Selivanov^‡

‡ Siberian Division of the Russian Academy of Sciences, Novosibirsk, Russia

Corresponding author: Svetlana Selivanova ( s_eliv@yahoo.com )

This article is freely available under the J.UCS Open Content License.

Citation: Selivanova S, Selivanov V (2009) Computing the Solution Operators of Symmetric Hyperbolic Systems of PDE. JUCS - Journal of Universal Computer Science 15(6): 1337-1364. https://doi.org/10.3217/jucs-015-06-1337

Abstract

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.

Keywords

hyperbolic system, PDE, computability, metric space, norm, matrix pencil, difference scheme, stability, finite-dimensional approximation