Symbolic-numerical methods for the computation of normal forms of PDEs

DOI10.1016/S0377-0427(03)00482-5zbMath1029.65055OpenAlexW2024977058MaRDI QIDQ1410877

Malidi Ahamadi, Jean-Jacques Gervais

Publication date: 15 October 2003

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(03)00482-5

zbMATH Keywords

finite element methodHopf bifurcationreaction-diffusion systemsemilinear parabolic equationevolution equationsBanach spacelocal bifurcationsMapleSymbolic computationMatlabCenter manifoldNormal formspitchfor, bifurcation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Abstract parabolic equations (35K90) Reaction-diffusion equations (35K57) Nonlinear differential equations in abstract spaces (34G20) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solutions to equations with nonlinear operators (65J15) Bifurcations in context of PDEs (35B32)

Related Items (1)

Construction of Bifurcation Diagrams Using POD on the Fly

Uses Software

• Maple
• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A simple global characterization for normal forms of singular vector fields
• Applications of centre manifold theory
• Singularities and groups in bifurcation theory. Volume II
• Symbolic computation of normal forms for semi-simple cases
• Application of the singular value decomposition to the numerical computation of the coefficients of amplitude equations and normal forms
• SPIRALS IN SCALAR REACTION–DIFFUSION EQUATIONS

This page was built for publication: Symbolic-numerical methods for the computation of normal forms of PDEs