On asymptotic expansions in nonlinear, singularly perturbed difference equations^∗

∗The work was supported by the DFG (German research association) through a scholarship at the Univ. of Maryland, College Park, U.S.A.

Abstract

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.

∗The work was supported by the DFG (German research association) through a scholarship at the Univ. of Maryland, College Park, U.S.A.

∗The work was supported by the DFG (German research association) through a scholarship at the Univ. of Maryland, College Park, U.S.A.

Notes

∗The work was supported by the DFG (German research association) through a scholarship at the Univ. of Maryland, College Park, U.S.A.

Additional information

Notes on contributors

Hans-Jüirgen Reinhardt