Laguerre approximation of stable manifolds with application to connecting orbits

DOI10.1090/S0025-5718-03-01535-7zbMath1033.65116OpenAlexW2091964333MaRDI QIDQ4433128

Gerald Moore

Publication date: 29 October 2003

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01535-7

zbMATH Keywords

algorithmnumerical experimentsinvariant manifoldserror boundssuperconvergencecollocationLaguerre polynomialshomoclinic orbitsstable manifoldspectral methodsautonomous system

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Invariant manifold theory for dynamical systems (37D10) Numerical nonlinear stabilities in dynamical systems (65P40) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items

A Hermite spectral method for the computation of homoclinic orbits and associated functionals ⋮ Orthogonal polynomial expansions for the matrix exponential ⋮ Numerical computation of connecting orbits in planar piecewise smooth dynamical system

Uses Software

• AUTO
• HomCont

Cites Work

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• Algorithms for constructing stable manifolds of stationary solutions
• A NUMERICAL TOOLBOX FOR HOMOCLINIC BIFURCATION ANALYSIS
• Computation and parametrization of periodic and connecting orbits
• Calculation of Gauss Quadrature Rules

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