Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation

DOI10.1016/J.CAM.2006.02.023zbMath1115.65118OpenAlexW2077477133MaRDI QIDQ875360

Teruya Minamoto, Mitsuhiro T. Nakao

Publication date: 13 April 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.02.023

zbMATH Keywords

numerical examplesfixed point theoremradially symmetric solutionperturbed Gelfand equationextended systemnumerical verification methoddouble turning pointtwo-parameter dependent nonlinear problem

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Algorithms with automatic result verification (65G20)

Related Items (8)

Rigorous verification of saddle-node bifurcations in ODEs ⋮ Numerical verification for solutions to partial differential equations ⋮ The bifurcation curves of a category of Dirichlet boundary value problems ⋮ Topological instabilities in families of semilinear parabolic problems subject to nonlinear perturbations ⋮ A theorem on S-shaped bifurcation curve for a positone problem with convex-concave nonlinearity and its applications to the perturbed Gelfand problem ⋮ Global smooth solution curves using rigorous branch following ⋮ Rigorous verification of Hopf bifurcations in functional differential equations of mixed type ⋮ Rigorous Verification of Hopf Bifurcations via Desingularization and Continuation

Uses Software

• PROFIL/BIAS

Cites Work

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