Approximating Evolution Operators for Delay Equations: A Convergence Framework
Analysis
This paper addresses the crucial problem of approximating the spectra of evolution operators for linear delay equations. This is important because it allows for the analysis of stability properties in nonlinear equations through linearized stability. The paper provides a general framework for analyzing the convergence of various discretization methods, unifying existing proofs and extending them to methods lacking formal convergence analysis. This is valuable for researchers working on the stability and dynamics of systems with delays.
Key Takeaways
- •Provides a general framework for analyzing the convergence of discretization methods for linear delay equations.
- •Unifies proofs for existing methods and extends them to methods without formal convergence analysis.
- •Useful for investigating the stability properties of nonlinear equations via linearized stability.
“The paper develops a general convergence analysis based on a reformulation of the operators by means of a fixed-point equation, providing a list of hypotheses related to the regularization properties of the equation and the convergence of the chosen approximation techniques on suitable subspaces.”