Singular Perturbation Techniques: A Comparison of the Method of Matched Asymptotic Expansions with that of Multiple Scales

SIAM Review ◽  
1977 ◽  
Vol 19 (3) ◽  
pp. 502-516 ◽  
Author(s):  
David J. Wollkind
Keyword(s):  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Multiple Scales ◽  
Matched Asymptotic Expansions ◽  
Perturbation Techniques

On the shape of small sessile and pendant drops by singular perturbation techniques

1991 ◽  
Vol 233 ◽  
pp. 519-537 ◽  
Author(s):  
S. B. G. O'Brien
Keyword(s):  
Boundary Layer ◽  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Numerical Results ◽  
Matched Asymptotic Expansions ◽  
Perturbation Techniques ◽  
Pendant Drop ◽  
Asymptotic Expressions ◽  
Good Agreement ◽  
Pendant Drops

The problem of obtaining asymptotic expressions describing the shape of small sessile and pendant drops is revisited. Both cases display boundary-layer behaviour and the method of matched asymptotic expansions is used to obtain solutions. These give good agreement when compared with numerical results. The sessile solutions are relatively straightforward, while the pendant drop displays a behaviour which is both rich and interesting.

On the method of matched asymptotic expansions

1969 ◽  
Vol 65 (1) ◽  
pp. 209-231 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Unknown Function ◽  
Singular Perturbation Problems ◽  
Matched Asymptotic Expansions ◽  
Uniform Approximations ◽  
Perturbation Problems ◽  
Asymptotic Matching

AbstractThe method of matched (or of ‘inner and outer’) asymptotic expansions is reviewed, with particular reference to two general techniques which have been proposed for ‘matching’; that is, for establishing a relationship between the inner and outer expansions, to finite numbers of terms, of an unknown function. It is shown that the first technique, which uses the idea of overlapping of the two expansions, can be difficult and laborious in some applications; while the second, which is the ‘asymptotic matching principle’ in the form stated by Van Dyke(13) can be incorrect. Two different sets of conditions sufficient for the validity of the asymptotic matching principle are then established, on the basis of assumptions about the structure of expressions which approximate to the desired function f(x,∈) for all relevant values of x. Finally, it is noted that in four classes of singular-perturbation problems for which complete and rigorous asymptotic theories exist, uniform approximations to the solutions have a structure which is a particular form of the general one assumed in this paper.

Singular Perturbation Techniques and Asymptotic Expansions for Some Complex Enzyme Reactions

2020 ◽  
pp. 43-53 ◽  
Author(s):  
Alberto Maria Bersani ◽  
Alessandro Borri ◽  
Alessandro Milanesi ◽  
Giovanna Tomassetti ◽  
Pierluigi Vellucci
Keyword(s):  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Perturbation Techniques ◽  
Enzyme Reactions

scholarly journals A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

2019 ◽  
Vol 10 (1) ◽  
pp. 162-181
Author(s):  
A. M. Bersani ◽  
A. Borri ◽  
A. Milanesi ◽  
G. Tomassetti ◽  
P. Vellucci
Keyword(s):  
Singular Perturbation ◽  
Enzyme Kinetics ◽  
Chemical Reaction ◽  
Asymptotic Expansions ◽  
Competitive Inhibition ◽  
Perturbation Techniques ◽  
Inhibitory Mechanisms ◽  
Perturbation Order ◽  
Study Case ◽  
Uniform Expansions

Abstract In this paper we study the model of the chemical reaction of fully competitive inhibition and determine the appropriate parameter ∊ (related to the chemical constants of the model), for the application of singular perturbation techniques. We determine the inner and the outer solutions up to the first perturbation order and the uniform expansions. Some numerical results are discussed.

Hydrodynamic Pressure Field on a Slender Ship Moving Over a High-Frequency Wavy Shallow Bottom

1976 ◽  
Vol 43 (2) ◽  
pp. 232-236 ◽  
Author(s):  
A. Plotkin
Keyword(s):  
Shallow Water ◽  
Asymptotic Expansions ◽  
Potential Flow ◽  
High Frequency ◽  
Pressure Field ◽  
Multiple Scales ◽  
Hydrodynamic Pressure ◽  
Order Effect ◽  
Wavy Wall ◽  
Perturbation Techniques

The hydrodynamic pressure field for the unsteady subcritical potential flow of a slender ship moving over a wavy wall in shallow water is analyzed using perturbation techniques. For the case of wall wavelength much smaller than the ship length but larger than the transverse ship dimensions, a combination of the methods of matched asymptotic expansions and multiple scales is used to obtain the lowest-order effect of the bottom variation.

Sign in / Sign up

Export Citation Format

Share Document