Single Perturbation Problems in Chemical Physics - Advances in Chemical Physics by John J H Miller Hardcover

Book Synopsis

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 ProblemsModeling 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 workof leading Russian researchers in singular perturbation theory andits application. Since boundary layers were first introduced byPrandtl early in this century, rapid advances have been made in theanalytic and numerical investigation of these phenomena, andnowhere have these advances been more notable than in the Russianschool of singular perturbation theory. The three chapters in thisvolume treat various aspects of singular perturbations and theirnumerical solution, and represent some of the best work done inthis area:
* The first chapter, "The Matching Method for Asymptotic Solutionsin Chemical Physics Problems," is concerned with the analysis ofsome singular perturbation problems that arise in chemicalkinetics. In this chapter the matching method is applied to findasymptotic solutions to some dynamical systems of ordinarydifferential equations whose solutions have multiscale timedependence.
* The second chapter, "Singularly Perturbed Problems with Boundaryand Interior Layers: Theory and Application," offers acomprehensive overview of the theory and application of asymptoticapproximations for many different kinds of problems in chemicalphysics governed by either ordinary or partial differentialequations with boundary and interior layers.
* The third chapter, "Numerical Methods for Singularly PerturbedBoundary Value Problems Modeling Diffusion Processes," discussesthe numerical difficulties that arise in solving the problemsdescribed in the first two chapters, and proposes rigorous criteriafor determining whether or not a numerical method is satisfactoryfor such problems. Methods satisfying these criteria are thenconstructed and applied to obtain numerical solutions to a range ofsample problems.

Timely, authoritative, and invaluable to researchers in all areasof chemical physics, Singular Perturbation Problems in ChemicalPhysics is an essential resource.

From the Back Cover

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.

About the Author

JOHN J. H. MILLER earned his PhD in numerical analysis at MIT. Henow teaches in the Department of Mathematics, Trinity College, Dublin, and conducts research at the Institute for NumericalComputation and Analysis, also in Dublin. His current researchinterests include fitted mesh and fitted operator methods forsolving singularly perturbed differential equations, and symbolicalgorithms for isolating the roots of polynomials.