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Singular Perturbation Analysis of Integral Equations: Part II
Author(s) -
Lange Charles G.,
Smith Donald R.
Publication year - 1993
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm19939011
Subject(s) - integral equation , classification of discontinuities , mathematics , mathematical analysis , method of matched asymptotic expansions , singular perturbation , volterra integral equation , jump , perturbation (astronomy) , asymptotic analysis , boundary value problem , physics , quantum mechanics
Singularly perturbed linear Volterra or Fredholm integral equations with kernels possessing jump discontinuities in a derivative are discussed within the framework of [6]. An intriguing and remarkable feature of such equations is that in general the leading order outer solution does not satisfy the unperturbed integral equation. Moreover, the solution usually exhibits large amplitude boundary layer behavior at one or both endpoints. Our perturbation technique, which is based on an efficient asymptotic splitting of the integral equation, clearly reveals the rich asymptotic solution structure for this class of equations.