Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

by Hans G. Kaper, Marc Garbey

Overview

Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per

Product Details

ISBN-13:	9781138441736
Publisher:	Taylor & Francis
Publication date:	07/27/2017
Series:	Lecture Notes in Pure and Applied Mathematics
Pages:	286
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

Hans G. Kaper, Argonne National Laboratory, Illinois. Marc Garbey, Universite Claude Bernard, Lyon, France.

Date of Birth:

September 27, 1948

Table of Contents

Preface; Part I: Singular Perturbation Methods. Singular Perturbations, Asymptotic Evaluation of Integrals, and Computational Challenges; Capture and the Connection Formulas for the Transition across a Separatrix Part II: Asymptotic-Induced Domain Decomposition. Domain Decomposition: An Instrument of Asymptotic-Numerical Methods; An Asymptotically Induced Domain Decomposition Method for Parabolic Boundary Layer Problems; Asymptotic-Induced Numerical Methods for Conservation Laws Part III: Perturbation Methods and Their Use in Numerical Computations. Asymptotic Analysis of Dissipative Waves with Applications to Their Numerical Simulation; A Hybrid Perturbation-Galerkin Technique for Partial Differential Equations; Part IV: Asymptotic Analysis in Physics. On the Equations of Physical Oceanography ; Transonics and Asymptotics; Evolution to Detonation in a Nonuniformly Heated Reactive Medium; Surface Evolution Equations from Detonation Theory; An Asymptotic Analysis of the Quantum Liouville Equation; Lattice Boltzmann Methods for Some 2-D Nonlinear Diffusion Equations: Computational Results Part V: Asymptotic Behavior of Nonlinear Partial Differential Equations. Blow-up of Solutions of Nonlinear Heat and Wave Equations; Convergence to Steady State of Solutions of Viscous Conservation Laws Part VI: Toward the Automation of Asymptotic Analysis. Symbolic Manipulation Software and the Study of Differential Equations

Editorial Reviews

Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular perturbation methods, asymptotic-induced domain decomposition, perturbation methods and their use in numerical computations, asymptotic analysis in physics, asymptotic behavior of nonlinear partial differential equations, and the prospects for the automation of asymptotic analysis. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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