On Matrix-Free Computation of 2D Unstable Manifolds

DOI10.1137/100789804zbMath1227.65066arXiv1003.4463OpenAlexW1976754705MaRDI QIDQ3095047

Lennaert Van Veen, Genta Kawahara, Matsumura Atsushi

Publication date: 28 October 2011

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.4463

zbMATH Keywords

algorithmperiodic solutionsboundary value problemCouette flowunstable manifoldmultiple shootingarclength continuationNewton-Krylov continuationorbit continuationshear turbulence

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Periodic solutions to ordinary differential equations (34C25) Shear flows and turbulence (76F10) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (9)

Computing heteroclinic orbits using adjoint-based methods ⋮ A parallel algorithm for the computation of invariant tori in large-scale dissipative systems ⋮ A Numerical Scheme for Computing Stable and Unstable Manifolds in Nonautonomous Flows ⋮ The onset of transient turbulence in minimal plane Couette flow ⋮ Vertically localised equilibrium solutions in large-eddy simulations of homogeneous shear flow ⋮ Heteroclinic path to spatially localized chaos in pipe flow ⋮ Continuation and stability of rotating waves in the magnetized spherical Couette system: secondary transitions and multistability ⋮ Continuation of Bifurcations of Periodic Orbits for Large-Scale Systems ⋮ Numerical Bifurcation Analysis in 3D Kolmogorov Flow Problem

Uses Software

• AUTO
• Trilinos
• AUTO-07P

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