Overview

An asymptotic expansion is a series that provides a sequence of increasingly accurate approximations to a function in a particular limit. The formal definition, given by Poincare (1886, Acta Math. 8:295), is as follows. Given a function,

Full Product Details

Author:   Harvey Segur ,  Saleh Tanveer ,  Herbert J. Levine
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1991
Volume:   284
Dimensions:   Width: 17.80cm , Height: 2.10cm , Length: 25.40cm
Weight:   0.773kg
ISBN:  

9781475704372

ISBN 10:   1475704372
Pages:   408
Publication Date:   02 June 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Asymptotology and Borel Summation.- Asymptotics, Superasymptotics, Hyperasymptotics.- Computation of Transcendental Effects in Growth Problems: Linear Solvability Conditions and Nonlinear Methods- The Example of the Geometric Model.- The Geometric Model of Crystal Growth.- The Geometric Model of Crystal Growth: An Overview.- Numerical Analysis of the Geometric Model for Dendritic Growth of Crystals.- Dendritic Crystal Growth.- Dendritic Crystal Growth-Overview.- An Experimental Assessment of Continuum Models of Dendritic Growth.- A New Formulation for Dendritic Crystal Growth in Two Dimensions.- Directional Solidification of Solids.- Directional Growth of Dilute Mixtures and Lamellar Eutectics.- A Flat Interface and Its Unfolding Bifurcations.- Flow in a Hele-Shaw Cell (Also known as VISCOUS FINGERING).- Viscous Displacement in a Hele-Shaw Cell.- Saffman-Taylor Viscous Fingering in a Wedge.- Saffman-Taylor Problem in a Sector Geometry.- The Rapidly Forced Pendulum.- Exponentially Small Estimate for Separatrix Splittings.- Exponentially Small Phenomena in the Rapidly Forced Pendulum.- Proof of An Asymptotic Symmetry of the Rapidly Forced Pendulum.- Ordinary Differential Equations.- Exponentially Small Oscillations in the Solution of an Ordinary Differential Equation.- Singular Perturbations of Solitons.- Reflection Coefficient Beyond All Orders for Singular Problems.- Laminar Flow in a Porous Channel.- Existence and Stability of Particle Channeling in Crystals on Time-Scales Beyond All Orders.- Solitary Water Waves in the Presence of Small Surface Tension.- Gravity-Capillary Free Surface Flows.- Solitary Waves With Ripples Beyond All Orders.- Generalized Solitary Waves in a Stratified Fluid.- Problems in Optics.- Bending Losses in Optical Fibers.- Exponential Asymptoticsand Spectral Theory for Curved Optical Waveguides.- Solitary Waves in Self-Induced Transparency.- Potpourri.- Exponential Asymptotics for Partial Differential Equations.- Problems of Existence of Nontopological Solitons (Breathers) for Nonlinear Klein-Gordon Equations.- Exponentially Small Residues Near Analytic Invariant Circles.- Asymptotics of Partial Differential and the Renormalization Group.

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