The Matching Method for Asymptotic Solutions in Chemical Physics
Problems by A. M. Il'in, L. A. Kalyakin, and S. I. Maslennikov
Singularly Perturbed Problems with Boundary and Interior Layers:
Theory and Application by V. F. Butuzov and A. B. Vasilieva
Numerical Methods for Singularly Perturbed Boundary Value Problems
Modeling Diffusion Processes by V. L. Kolmogorov and G. I. Shishkin
An important addition to the Advances in Chemical Physics series,
this volume makes available for the first time in English the work
of leading Russian researchers in singular perturbation theory and
its application. Since boundary layers were first introduced by
Prandtl early in this century, rapid advances have been made in the
analytic and numerical investigation of these phenomena, and
nowhere have these advances been more notable than in the Russian
school of singular perturbation theory. The three chapters in this
volume treat various aspects of singular perturbations and their
numerical solution, and represent some of the best work done in
this area:
* The first chapter, "The Matching Method for Asymptotic Solutions
in Chemical Physics Problems," is concerned with the analysis of
some singular perturbation problems that arise in chemical
kinetics. In this chapter the matching method is applied to find
asymptotic solutions to some dynamical systems of ordinary
differential equations whose solutions have multiscale time
dependence.
* The second chapter, "Singularly Perturbed Problems with Boundary
and Interior Layers: Theory and Application," offers a
comprehensive overview of the theory and application of asymptotic
approximations for many different kinds of problems in chemical
physics governed by either ordinary or partial differential
equations with boundary and interior layers.
* The third chapter, "Numerical Methods for Singularly Perturbed
Boundary Value Problems Modeling Diffusion Processes," discusses
the numerical difficulties that arise in solving the problems
described in the first two chapters, and proposes rigorous criteria
for determining whether or not a numerical method is satisfactory
for such problems. Methods satisfying these criteria are then
constructed and applied to obtain numerical solutions to a range of
sample problems.
Timely, authoritative, and invaluable to researchers in all
areas of chemical physics, Singular Perturbation Problems in
Chemical Physics is an essential resource.
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