On asymptotic expansions in nonlinear, singularly perturbed difference equations*
作者:
Hans-Jüirgen Reinhardt,
期刊:
Numerical Functional Analysis and Optimization
(Taylor Available online 1979)
卷期:
Volume 1,
issue 6
页码: 565-587
ISSN:0163-0563
年代: 1979
DOI:10.1080/01630567908816035
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
The present paper deals with the problem of constructing and proving asymptotic expansions for nonlinear, singularly perturbed difference equations. New methods for the construction of asymptotic expansions are presented and compared with well-known ones. For the proof of their validity, fundamental principles for the treatment of nonlinear singular perturbation problems are applied, based on the concepts of e-stability, formal asymptotic expansions, matching and asymptotic expansions. The results are derived from a general theory of asymptotic expansions of nonlinear operator equations that has been developed recently by the author.
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