Bit Complexity of Computing Solutions for Symmetric Hyperbolic Systems of PDEs with Guaranteed Precision

TL;DR

This paper analyzes the bit complexity involved in computing solutions for symmetric hyperbolic PDE systems, providing upper bounds and building on prior work in computability within rigorous analysis.

Contribution

It establishes upper bounds on the bit complexity of solution operators for symmetric hyperbolic PDEs, advancing the understanding of their computational feasibility.

Findings

Derived upper bounds for bit complexity of solution operators

Extended previous computability results to symmetric hyperbolic systems

Provided a framework for analyzing computational resources in PDE solutions

Abstract

We establish upper bounds of bit complexity of computing solution operators for symmetric hyperbolic systems of PDEs. Here we continue the research started in in our revious publications where computability, in the rigorous sense of computable analysis, has been established for solution operators of Cauchy and dissipative boundary-value problems for such systems.