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,
Inhaltsverzeichnis
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.
