Layer Resolving Grids and Transformations for Singular Perturbation Problems

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VSP, 2001 - Mathematics - 284 pages
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The approach of layer-damping coordinate transformations to treat singularly perturbed equations is a relatively new, and fast growing area in the field of applied mathematics. This monograph aims to present a clear, concise, and easily understandable description of the qualitative properties of solutions to singularly perturbed problems as well as of the essential elements, methods and codes of the technology adjusted to numerical solutions of equations with singularities by applying layer-damping coordinate transformations and corresponding layer-resolving grids.
The first part of the book deals with an analytical study of estimates of the solutions and their derivatives in layers of singularities as well as suitable techniques for obtaining results. In the second part, a technique for building the coordinate transformations eliminating boundary and interior layers, is presented. Numerical algorithms based on the technique which is developed for generating layer-damping coordinate transformations and their corresponding layer-resolving meshes are presented in the final part of this volume.
This book will be of value and interest to researchers in computational and applied mathematics.
 

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Contents

Introduction to singularly perturbed problems
1
Background for qualitative analysis
37
Estimates of the solution derivatives to semilinear problems
65
Problems for ordinary quasilinear equations
115
Systems of ordinary differential equations
149
Generation of transformations and layerresolving grids
183
Analysis of numerical algorithms
227
References
270
Index
283
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