Geometry of the Computational Singular Perturbation Method

Geometry of the Computational Singular Perturbation Method

The Computational Singular Perturbation (CSP) method, developed by Lam and Goussis [Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1988, pp. 931–941], is a commonly-used method for finding approximations of slow manifolds in systems of ordinary differential equations (ODEs) with multiple time scales. The validity of the CSP method was established fo...

Fast and Slow Dynamics for the Computational Singular Perturbation Method

The Computational Singular Perturbation CSP method of Lam and Goussis is an iterative method to reduce the dimensionality of systems of ordinary di erential equations with multiple time scales In J Nonlin Sci to appear the authors showed that each iteration of the CSP algorithm improves the approxima tion of the slow manifold by one order In this paper it is shown that the CSP method simultaneo...

Analysis of the Computational Singular Perturbation Reduction Method for Chemical Kinetics

This article is concerned with the asymptotic accuracy of the Computational Singular Perturbation (CSP) method developed by Lam and Goussis [The CSP method for simplifying kinetics, Int. J. Chem. Kin. 26 (1994) 461–486] to reduce the dimensionality of a system of chemical kinetics equations. The method, which is generally applicable to multiple-time scale problems arising in a broad array of sc...

Numerical Integration Scheme Using Singular Perturbation Method

Some multi degree-of-freedom dynamical systems exhibit a response that contain fast and slow variables. An example of such systems is a multibody system with rigid and deformable bodies. Standard numerical integration of the resultant equations of motion must adjust the time step according to the frequency of the fastest variable. As a result, the computation time is sacrificed. The singular pe...

The Stochastic Perturbation Method for Computational Mechanics