On the Asymptotic and Numerical Analysis of Exponentially Ill-Conditioned Singularly Perturbed Boundary Value Problems (1995)
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BibTeX
@MISC{Lee95onthe,
author = {June-Yub Lee and Michael J. Ward},
title = {On the Asymptotic and Numerical Analysis of Exponentially Ill-Conditioned Singularly Perturbed Boundary Value Problems},
year = {1995}
}
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Abstract
Asymptotic and numerical methods are used to study several classes of singularly perturbed boundary value problems for which the underlying homogeneous operators have exponentially small eigenvalues. Examples considered include the familiar boundary layer resonance problems and some extensions, and certain linearized equations associated with metastable internal layer motion. For the boundary layer resonance problems, a systematic projection method, motivated by the work of De Groen [SIAM J. Math. Anal. 11, (1980), pp. 1-22], is used to analytically calculate high order asymptotic solutions. This method justifies and extends some previous results obtained from the variational method of Grasman and Matkowsky [SIAM J. Appl. Math. 32, (1977), pp. 588-597]. A numerical approach, based on an integral equation formulation, is used to accurately compute boundary layer resonance solutions and their associated exponentially small eigenvalues. For various examples, the numerical results are show...
