Asymptotic Analysis and the Numerical Solution of Partial Differential Equations

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CRC Press, Feb 25, 1991 - Mathematics - 286 pages
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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
 

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Contents

Singular Perturbations Asymptotic Evaluation of Integrals and Computational Challenges
3
Capture and the Connection Formulas for the Transition across a Separatrix
17
AsymptoticInduced Domain Decomposition
31
An Instrument of AsymptoticNumerical Methods
33
An Asymptotically Induced Domain Decomposition Method for Parabolic Boundary Layer Problems
55
AsymptoticInduced Numerical Methods for Conservation Laws
75
Perturbation Methods and Their Use in Numerical Computations
97
Asymptotic Analysis of Dissipative Waves with Applications to Their Numerical Simulation
99
Evolution to Detonation in a Nonuniformly Heated Reactive Medium
161
Surface Evolution Equations from Detonation Theory
175
An Asymptotic Analysis of the Quantum Liouville Equation
185
Nonlinear Diffusion Equations Computational Results
197
Asymptotic Behavior of Nonlinear Partial Differential Equations
215
Wave Equations
217
Convergence to Steady State of Solutions of Viscous Conservation Laws
225
Toward the Automation of Asymptotic Analysis
239

A Hybrid PerturbationGalerkin Technique for Partial Differential Equations
113
Asymptotic Analysis in Physics
135
On the Equations of Physical Oceanography
137
Transonics and Asymptotics
145
Symbolic Manipulation Software and the Study of Differential Equations
241
Index
267
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