Large-Scale Continuation and Numerical Bifurcation for Partial Differential Equations

DOI10.1137/S0036142994273288zbMath0894.65023MaRDI QIDQ4377525

Bryan D. Davidson

Publication date: 10 February 1998

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

zbMATH Keywords

performancestabilitynumerical examplespreconditioningHopf bifurcationiterative methodmethod of linescontinuation algorithmbifurcation diagramequilibrium solutionrecursive projection methodlarge stiff systemssparse continuationsteady state systems

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items (8)

A simple solution of the Bratu problem ⋮ Continuation of invariant subspaces via the recursive projection method. ⋮ Krylov methods and determinants for detecting bifurcations in one parameter dependent partial differential equations ⋮ On the integral solution of the one-dimensional Bratu problem ⋮ Improvement of the recursive projection method for linear iterative scheme stabilization based on an approximate eigenvalue problem ⋮ Conjugate gradient type methods for semilinear elliptic problems with symmetry ⋮ CONTINUATION FOR NONLINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS DISCRETIZED BY THE MULTIQUADRIC METHOD ⋮ A continuation BSOR-Lanczos--Galerkin method for positive bound states of a multi-component Bose-Einstein condensate

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