Some Numerical Aspects of Computing Inertial Manifolds

DOI10.1137/0914002zbMath0781.65101OpenAlexW2035506178MaRDI QIDQ5286332

Manfred R. Trummer, Robert D. Russell, David M. Sloan

Publication date: 29 June 1993

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

Full work available at URL: https://doi.org/10.1137/0914002

zbMATH Keywords

Galerkin methodevolution equationdifferential-algebraic equationsKuramoto-Sivashinsky equationNewton methodspectral methodPicard iterationreaction diffusion equationinertial manifoldsNumerical testsdissipative partial differential equationsinertial form

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Applications to the sciences (65Z05) Initial value problems for linear higher-order PDEs (35G10) Bifurcations in context of PDEs (35B32) Higher-order parabolic equations (35K25)

Related Items (13)

Finite-dimensional behavior in dissipative partial differential equations ⋮ A finite difference scheme for computing inertial manifolds ⋮ On the effectiveness of the approximate inertial manifold -- a computational study ⋮ On computing the long-time solution of the two-dimensional Navier-Stokes equations ⋮ Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation ⋮ On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation ⋮ A step-size selection strategy for explicit Runge-Kutta methods based on Lyapunov exponent theory ⋮ Linear system solvers for boundary value ODEs ⋮ Bifurcation computations on an approximate inertial manifold for the 2D Navier-Stokes equations ⋮ An exact solution to the Kuramoto-Sivashinsky equation ⋮ Exact solutions of some nonlinear evolution equations using symbolic computations ⋮ Convergence of a chaotic attractor with increased spatial resolution of the Ginzburg-Landau equation. ⋮ Time-marching on the slow manifold: The relationship between the nonlinear Galerkin method and implicit timestepping algorithms

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