Continuation and Local Perturbation for Multiple Bifurcations

DOI10.1137/0907085zbMath0617.65056OpenAlexW1992806809MaRDI QIDQ4727304

Cheng-Sheng Chien, Eugene L. Allgower

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1137/0907085

zbMATH Keywords

Banach spacesnumerical resultsSard's theoremnonlinear eigenvalue problemcontinuation methodsbifurcation curvessmooth mappingmultiple bifurcationgradient maps

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Numerical solutions to equations with nonlinear operators (65J15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (20)

Bifurcations of corank greater than two ⋮ Continuation-minimization methods for stability problems ⋮ An efficient algorithm for the Schrödinger-Poisson eigenvalue problem ⋮ Generic movement of eigenvalues for equivariant self-adjoint matrices ⋮ Spectral collocation and a two-level continuation scheme for dipolar Bose-Einstein condensates ⋮ Conjugate gradient and minimal residual method for solving symmetric indefinite systems ⋮ Conjugate gradient methods for continuation problems. II ⋮ Bifurcations of the von Kármán equations with Robin boundary conditions ⋮ Path following around corank-2 bifurcation points of a semi-linear elliptic problem with symmetry ⋮ The spectral method and numerical continuation algorithm for the von Kármán problem with postbuckling behaviour of solutions ⋮ Conjugate gradient methods for continuation problems ⋮ A MULTIGRID-LANCZOS ALGORITHM FOR THE NUMERICAL SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ⋮ Generalized Lyapunov-Schmidt reduction for parametrized equations at near singular points ⋮ On the numerical solution of double-periodic elliptic eigenvalue problems ⋮ Large sparse continuation problems ⋮ Secondary bifurcations in the buckling problem ⋮ Multi-parameter continuation and collocation methods for rotating multi-component Bose–Einstein condensates ⋮ On a numerical Lyapunov-Schmidt method for operator equations ⋮ Bifurcations of a simplified buckling problem and the effect of discretizations ⋮ A parallel continuation algorithm for nonlinear eigenvalue problems

Uses Software

• PITCON

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