MULTIGRID-CONJUGATE GRADIENT TYPE METHODS FOR REACTION–DIFFUSION SYSTEMS

DOI10.1142/S0218127404011466zbMath1064.65040OpenAlexW2006165827MaRDI QIDQ4655736

Huei-Shuang Chen, Cheng-Sheng Chien, Shing-Lin Chang

Publication date: 8 March 2005

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127404011466

zbMATH Keywords

algorithmsnumerical resultsbifurcationfinite differencesGMRESmultigrid methodscontinuation methodsnonlinear elliptic eigenvalue problemReaction-diffusion systemsnearly singular systemsBi-CGSTAB\(W\)-cycle\(V\)-cycle

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Reaction-diffusion equations (35K57) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

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Cites Work

• Unnamed Item
• Multiple bifurcations in a reaction-diffusion problem
• Degenerate bifurcations near a double eigenvalue in the Brusselator
• GMRES On (Nearly) Singular Systems
• Multi-Grid Solution of Bifurcation Problems
• Multigrid Bifurcation Iteration
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A Multigrid Continuation Method for Elliptic Problems with Folds
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Arc-Length Continuation and Multigrid Techniques for Nonlinear Elliptic Eigenvalue Problems
• Preconditioned Iterative Methods for Homotopy Curve Tracking
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• On the Computation of Approximate Eigenvalues and Eigenfunctions of Elliptic Operators by Means of a Multi-Grid Method
• A Multigrid Tutorial, Second Edition
• A MULTIGRID-LANCZOS ALGORITHM FOR THE NUMERICAL SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS
• Numerical Methods for Bifurcations of Dynamical Equilibria