A functional analytic approach to validated numerics for eigenvalues of delay equations
From MaRDI portal
Publication:2192455
DOI10.3934/jcd.2020005OpenAlexW3011212908MaRDI QIDQ2192455
Jean-Philippe Lessard, Jason D. Mireles James
Publication date: 17 August 2020
Published in: Journal of Computational Dynamics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/jcd.2020005
Stability theory of functional-differential equations (34K20) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Algorithms with automatic result verification (65G20) Index theory for dynamical systems, Morse-Conley indices (37B30) Spectral theory of functional-differential operators (34K08)
Related Items
Parameterization of unstable manifolds for DDEs: formal series solutions and validated error bounds, Eigenvalues and delay differential equations: periodic coefficients, impulses and rigorous numerics, Numerical Computation of Transverse Homoclinic Orbits for Periodic Solutions of Delay Differential Equations, Pseudospectral Approximation of Hopf Bifurcation for Delay Differential Equations, Rigorous verification of Hopf bifurcations in functional differential equations of mixed type, Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow
- Existence and stability of traveling pulse solutions of the FitzHugh-Nagumo equation
- A prototype model for chaos studies
- High-dimensional chaotic behavior in systems with time-delayed feedback
- A simple chaotic delay differential equation
- Non-symmetric low-index solutions for a symmetric boundary value problem
- Delay differential equations: with applications in population dynamics
- On hyperbolicity in the renormalization of near-critical area-preserving maps
- Error bounds for computed eigenvalues and eigenvectors. II
- Periodic solutions of some nonlinear autonomous functional differential equations
- Error bounds for computed eigenvalues and eigenvectors
- On eigenvector bounds
- Eigenvalue computation in the 20th century
- Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation
- Fourier-Taylor approximation of unstable manifolds for compact maps: numerical implementation and computer-assisted error bounds
- Computer-assisted proofs for radially symmetric solutions of PDEs
- Spectral stability for the wave equation with periodic forcing
- On a model of a currency exchange rate -- local stability and periodic solutions
- Rigorous numerics for NLS: bound states, spectra, and controllability
- Numerical verifications for eigenvalues of second-order elliptic operators
- Stability and uniqueness of slowly oscillating periodic solutions to Wright's equation
- Rigorous Numerics in Floquet Theory: Computing Stable and Unstable Bundles of Periodic Orbits
- Verification methods: Rigorous results using floating-point arithmetic
- Bounds on Real Eigenvalues and Singular Values of Interval Matrices
- Numerical proof of stability of viscous shock profiles
- A method to rigorously enclose eigendecompositions of interval matrices
- Pseudospectral Discretization of Nonlinear Delay Equations: New Prospects for Numerical Bifurcation Analysis
- INFINITE DIMENSIONAL KRAWCZYK OPERATOR FOR FINDING PERIODIC ORBITS OF DISCRETE DYNAMICAL SYSTEMS
- A computer-assisted instability proof for the Orr-Sommerfeld problem with Poiseuille flow
- A Test for Existence of Solutions to Nonlinear Systems
- Computing the characteristic roots for delay differential equations
- Computer-Assisted Proof of Heteroclinic Connections in the One-Dimensional Ohta--Kawasaki Model
- Oscillation and Chaos in Physiological Control Systems
- Eigenvalue excluding for perturbed-periodic one-dimensional Schrödinger operators
- Applied Delay Differential Equations
- Pseudospectral Differencing Methods for Characteristic Roots of Delay Differential Equations
- Verified Computations of Eigenvalue Exclosures for Eigenvalue Problems in Hilbert Spaces
- The Newton-Kantorovich Theorem
- A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto--Sivashinsky PDE
- An Introduction to Delay Differential Equations with Applications to the Life Sciences
- Computational error bounds for multiple or nearly multiple eigenvalues
- Stability and bifurcation for a delayed predator-prey model and the effect of diffusion
