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Method of matched asymptotic expansions

About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, four different structures of identifying the singular perturbation parameter are presented and various features of these structures are discussed and further investigations are explored in identifying the SPM by using non-dimensional forms for the nonlinear dynamical equations.

17 citations

Journal ArticleDOI
TL;DR: It is shown that this method provides uniformly convergent solutions with respect to the small perturbation parameter, but, if the time step is sufficiently large, then the roots of the characteristic polynomial that defines the exponential solutions of the homogeneous differential equation may become nearly independent of the timestep and the solution may exhibit large errors.

17 citations

Book
18 Jul 2013
TL;DR: Inverse Functions Dominant Balance Asymptotics of Integrals Integrating Taylor Series Repeated Integration by Parts Laplace's Method Review of Complex Numbers Method of Stationary Phase Method of Steepest Descents Speeding Up Convergence Shanks Transformation Richardson Extrapolation Euler Summation Borel Summations Continued Fraction Pade Approximants Differential Equations Classification of Differential Eq. 1.
Abstract: Introduction to Asymptotics Basic Definitions Limits via Asymptotics Asymptotic Series Inverse Functions Dominant Balance Asymptotics of Integrals Integrating Taylor Series Repeated Integration by Parts Laplace's Method Review of Complex Numbers Method of Stationary Phase Method of Steepest Descents Speeding Up Convergence Shanks Transformation Richardson Extrapolation Euler Summation Borel Summation Continued Fractions Pade Approximants Differential Equations Classification of Differential Equations First Order Equations Taylor Series Solutions Frobenius Method Asymptotic Series Solutions for Differential Equations Behavior for Irregular Singular Points Full Asymptotic Expansion Local Analysis of Inhomogeneous Equations Local Analysis for Nonlinear Equations Difference Equations Classification of Difference Equations First Order Linear Equations Analysis of Linear Difference Equations The Euler-Maclaurin Formula Taylor-Like and Frobenius-Like Series Expansions Perturbation Theory Introduction to Perturbation Theory Regular Perturbation for Differential Equations Singular Perturbation for Differential Equations Asymptotic Matching WKBJ Theory The Exponential Approximation Region of Validity Turning Points Multiple-Scale Analysis Strained Coordinates Method (Poincare-Lindstedt) The Multiple-Scale Procedure Two-Variable Expansion Method Appendix: Guide to the Special Functions Answers to Odd-Numbered Problems Bibliography Index

17 citations

Journal ArticleDOI
TL;DR: Miller's recurrence algorithm for tabulating the subdominant solution of a second-order difference equation is modified so as to take the asymptotic behaviour of the solution into account as discussed by the authors.
Abstract: Miller's recurrence algorithm for tabulating the subdominant solution of a second-order difference equation is modified so as to take the asymptotic behaviour of the solution into account. The asymptotic solutions of various types of equations are listed, and a method is given for estimating the error in the tabulated solution.

17 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202244
202110
202023
201913
201835