Root Following in Evans Function Computation
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Publication:3195248
DOI10.1137/140975590zbMath1326.65157OpenAlexW1878147714MaRDI QIDQ3195248
Joshua Lytle, Jeffrey Humpherys
Publication date: 22 October 2015
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/140975590
Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)
Related Items (6)
Nonlinear Eigenvalue Methods for Linear Pointwise Stability of Nonlinear Waves ⋮ Euler Versus Lagrange: The Role of Coordinates in Practical Evans-Function Computations ⋮ The Wentzel-Kramers-Brillouin approximation of semiclassical eigenvalues of the Zakharov–Shabat problem ⋮ Evans function computation for the stability of travelling waves ⋮ Spectra of Short Pulse Solutions of the Cubic-Quintic Complex Ginzburg-Landau Equation near Zero Dispersion ⋮ Transverse bifurcation of viscous slow MHD shocks
Uses Software
Cites Work
- Finding eigenvalues of holomorphic Fredholm operator pencils using boundary value problems and contour integrals
- Detecting exponential dichotomy on the real line: SVD and QR algorithms
- Time-stepping and preserving orthonormality
- Stability and instability of solitary waves of the fifth-order KdV equation: a numerical framework
- Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves
- Stability of isentropic Navier-Stokes shocks in the high-Mach number limit
- Semiclassical eigenvalue distribution of the Zakharov-Shabat eigenvalue problem
- Stability of viscous shocks in isentropic gas dynamics
- Spectral stability of ideal-gas shock layers
- Exponential dichotomy on the real line: SVD and QR methods
- An automatic orthonormalization method for solving stiff boundary-value problems
- The compound matrix method for ordinary differential systems
- A family of embedded Runge-Kutta formulae
- Numerical solution of Orr-Sommerfeld-type equations
- Geometric theory of semilinear parabolic equations
- On the numerical solution of the Orr-Sommerfeld problem: Asymptotic initial conditions for shooting methods
- A numerical method for linear two-point boundary-value problems using compound matrices
- Dichotomies in stability theory
- An initial value method for eigenvalue problems using compound matrices
- Stabilization of DAEs and invariant manifolds
- Perturbation theory for linear operators.
- Stability of bright solitary-wave solutions to perturbed nonlinear Schrödinger equations
- Exponential dichotomies and transversal homoclinic points
- Numerical exterior algebra and the compound matrix method
- Spectral and dynamical stability of nonlinear waves
- Efficient computation of analytic bases in Evans function analysis of large systems
- An efficient shooting algorithm for Evans function calculations in large systems
- Numerical testing of the stability of viscous shock waves
- Grassmannian spectral shooting
- A local greedy algorithm and higher-order extensions for global numerical continuation of analytically varying subspaces
- Continuation of Invariant Subspaces in Large Bifurcation Problems
- On the Error in QR Integration
- A New Basis Implementation for a Mixed Order Boundary Value ODE Solver
- Pointwise semigroup methods and stability of viscous shock waves
- Unitary Integrators and Applications to Continuous Orthonormalization Techniques
- Evans Function Stability of Combustion Waves
- Eigenvalues, and instabilities of solitary waves
- Spectral Behavior of Combustion Fronts with High Exothermicity
- Recipes for Continuation
- Stability of Traveling Waves for a Class of Reaction-Diffusion Systems That Arise in Chemical Reaction Models
- Viscous Hyperstabilization of Detonation Waves in One Space Dimension
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