ANALYSIS OF REDUCTION METHODS FOR MULTISCALE PROBLEMS

[1]  Ulrich Maas,et al.  Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space , 1992 .

[2]  H. M. Tsuchiya,et al.  On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics☆ , 1967 .

[3]  Ioannis G. Kevrekidis,et al.  Equation-free: The computer-aided analysis of complex multiscale systems , 2004 .

[4]  Epaminondas Mastorakos,et al.  Global reduced mechanisms for methane and hydrogen combustion with nitric oxide formation constructed with CSP data , 1999 .

[5]  Michael J. Davis,et al.  Geometric investigation of low-dimensional manifolds in systems approaching equilibrium , 1999 .

[6]  A. N. Gorban,et al.  Constructive methods of invariant manifolds for kinetic problems , 2003 .

[7]  Ioannis G. Kevrekidis,et al.  Constraint-Defined Manifolds: a Legacy Code Approach to Low-Dimensional Computation , 2005, J. Sci. Comput..

[8]  Alexander N Gorban,et al.  Invariant grids for reaction kinetics , 2003 .

[9]  Hans G. Kaper,et al.  Analysis of the Computational Singular Perturbation Reduction Method for Chemical Kinetics , 2004, J. Nonlinear Sci..

[10]  L. A. Segel,et al.  The Quasi-Steady-State Assumption: A Case Study in Perturbation , 1989, SIAM Rev..

[11]  Simon J. Fraser,et al.  The steady state and equilibrium approximations: A geometrical picture , 1988 .

[12]  B O Palsson,et al.  Mathematical modelling of dynamics and control in metabolic networks. I. On Michaelis-Menten kinetics. , 1984, Journal of theoretical biology.

[13]  Alexander N. Gorban,et al.  Method of invariant manifolds and regularization of acoustic spectra , 1994 .

[14]  J. Carr Applications of Centre Manifold Theory , 1981 .

[15]  Ioannis G. Kevrekidis,et al.  Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes , 2005, SIAM J. Appl. Dyn. Syst..

[16]  J. R. E. O’Malley Singular perturbation methods for ordinary differential equations , 1991 .

[17]  M. Neophytou,et al.  Reduced chemical mechanisms for atmospheric pollution using Computational Singular Perturbation analysis , 2004 .

[18]  Habib N. Najm,et al.  CSP analysis of a transient flame-vortex interaction: time scales and manifolds , 2003 .

[19]  Christopher Jones,et al.  Geometric singular perturbation theory , 1995 .

[20]  C. W. Gear,et al.  Equation-Free, Coarse-Grained Multiscale Computation: Enabling Mocroscopic Simulators to Perform System-Level Analysis , 2003 .

[21]  A. Fordy APPLICATIONS OF LIE GROUPS TO DIFFERENTIAL EQUATIONS (Graduate Texts in Mathematics) , 1987 .

[22]  Hans G. Kaper,et al.  Fast and Slow Dynamics for the Computational Singular Perturbation Method , 2004, Multiscale Model. Simul..

[23]  Mauro Valorani,et al.  Explicit time-scale splitting algorithm for stiff problems: auto-ignition of gaseous mixtures behind a steady shock , 2001 .

[24]  Marc R. Roussel,et al.  Geometry of the steady-state approximation: Perturbation and accelerated convergence methods , 1990 .

[25]  B. Schutz,et al.  Geometrical Methods of Mathematical Physics , 1998 .

[26]  Tamás Turányi,et al.  On the error of the quasi-steady-state approximation , 1993 .

[27]  A. Fersht Enzyme structure and mechanism , 1977 .

[28]  Neil Fenichel Geometric singular perturbation theory for ordinary differential equations , 1979 .

[29]  Hans G. Kaper,et al.  Asymptotic analysis of two reduction methods for systems of chemical reactions , 2002 .

[30]  Matthias Stiefenhofer Quasi-steady-state approximation for chemical reaction networks , 1998 .

[31]  S. H. Lam,et al.  Understanding complex chemical kinetics with computational singular perturbation , 1989 .

[32]  S. Lam,et al.  The CSP method for simplifying kinetics , 1994 .

[33]  Kenneth D. Mease,et al.  Geometry of Computational Singular Perturbations , 1995 .

[34]  Samuel Paolucci,et al.  On slow manifolds of chemically reactive systems , 2002 .

[35]  Iliya V. Karlin,et al.  Method of invariant manifold for chemical kinetics , 2003 .

[36]  C. Law,et al.  Complex CSP for chemistry reduction and analysis , 2001 .

[37]  Bernhard O. Palsson,et al.  On the dynamics of the irreversible Michaelis-Menten reaction mechanism , 1987 .

[38]  S. H. Lam,et al.  Using CSP to Understand Complex Chemical Kinetics , 1993 .

[39]  B. Dubrovin,et al.  Modern geometry--methods and applications , 1984 .

[40]  S. H. Lam,et al.  A study of homogeneous methanol oxidation kinetics using CSP , 1992 .