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Asymptotic Methods
In this final chapter, we will review methods for analyzing the behavior of functions defined by integrals in various neighborhoods, e.g., infinity....
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Block Preconditioning Methods for Asymptotic Preserving Scheme Arising in Anisotropic Elliptic Problems
Efficient and robust iterative solvers for strongly anisotropic elliptic equations are very challenging. Indeed, the discretization of this class of...
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Asymptotic preserving methods for quasilinear hyperbolic systems with stiff relaxation: a review
Hyperbolic systems with stiff relaxation constitute a wide class of evolutionary partial differential equations which describe several physical...
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High-order asymptotic methods provide accurate, analytic solutions to intractable potential problems
The classical problem of determining the density and capacity of arrays of potential sources is studied. This corresponds to a wide variety of...
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Non-asymptotic superlinear convergence of standard quasi-Newton methods
In this paper, we study and prove the non-asymptotic superlinear convergence rate of the Broyden class of quasi-Newton algorithms which includes the...
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Asymptotic Errors in the Superconvergence of Discontinuous Galerkin Methods Based on Upwind-Biased Fluxes for 1D Linear Hyperbolic Equations
In this paper, we study the superconvergence of the semi-discrete discontinuous Galerkin (DG) method for linear hyperbolic equations in one spatial...
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Asymptotic Expansion
This chapter concerns the basics of the asymptotic expansionAsymptotic expansion of a function.
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High order hybrid asymptotic augmented finite volume methods for nonlinear degenerate wave equations
In this paper, we provide high order hybrid asymptotic augmented finite volume schemes on a uniform grid for nonlinear weakly degenerate and strongly...
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Rates of Convergence to Non-degenerate Asymptotic Profiles for Fast Diffusion via Energy Methods
This paper is concerned with a quantitative analysis of asymptotic behaviors of (possibly sign-changing) solutions to the Cauchy–Dirichlet problem...
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The large-sample asymptotic behaviour of quartet-based summary methods for species tree inference
Summary methods seek to infer a species tree from a set of gene trees. A desirable property of such methods is that of statistical consistency; that...
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Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: A Review and Extensions of Tests for the Painlevé Property
The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity...
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Formally verified asymptotic consensus in robust networks
Distributed architectures are used to improve performance and reliability of various systems. Examples include drone swarms and load-balancing...
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A closed-form bound on the asymptotic linear convergence of iterative methods via fixed point analysis
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with...
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On the Asymptotic Convergence and Acceleration of Gradient Methods
We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special...
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Morphology of Kinetic Asymptotic Grids
This paper investigates the kinetic behaviour of asymptotic lamella grids with variable surface topology. The research is situated in the field of...
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Faster Asymptotic Solutions for N-Mixtures on Large Populations
We derive an asymptotic likelihood function for open-population N -mixture models and show that it has favorable computational complexity and accuracy...
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Asymptotic Safety and Cosmology
The asymptotic safety approach to quantum gravity provides a possible solution to the problem of the quantization of the gravitational field. It is...
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Asymptotic Expansions and Summability Application to Partial Differential Equations
This book provides a comprehensive exploration of the theory of summability of formal power series with analytic coefficients at the origin of Cn,...
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Improving Asymptotic Series
It becomes more and more tedious to obtain analytically the higher order corrections, even when the successive orders are linear. The methods...
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Integrated Asymptotic Approach to the Structural Mechanics Models
Methods for calculating multi-element structures are discussed, in which the calculation of the frame and the local stress-strain state in the joints...