Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

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

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