Single Perturbation Problems in Chemical Physics Analytic and Computational Methods, Volume 97

The Matching Method for Asymptotic Solutions in Chemical Physics Problems by A. M. Il'in, L. A. Kalyakin, and S. I. MaslennikovSingularly Perturbed Problems with Boundary and Interior Layers: Theory and Application by V. F. Butuzov and A. B. VasilievaNumerical Methods for Singularly Perturbed Boundary Value Problems Modeling Diffusion Processes by V. L. Kolmogorov and G. I. ShishkinAn 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.

About the editor JOHN J. H. MILLER earned his PhD in numerical analysis at MIT. He now teaches in the Department of Mathematics, Trinity College, Dublin, and conducts research at the Institute for Numerical Computation and Analysis, also in Dublin. His current research interests include fitted mesh and fitted operator methods for solving singularly perturbed differential equations, and symbolic algorithms for isolating the roots of polynomials.