Abstract
Nonlinear singularly perturbed boundary-value problems are considered, with one or two boundary layers but no turning points. The theory of differential inequalities is used to obtain a numerical procedure for quasilinear and semilinear problems. The required solution is approximated by combining the solutions of suitable auxiliary initial-value problems easily deduced from the given problem. From the numerical results, the method seems accurate and solutions to problems with extremely thin layers can be obtained at reasonable cost.
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Communicated by I. Galligani
This work was supported by CNR, Rome, Italy (Progetto Finalizzato Sistemi Informatici e Calcolo Parallelo, Sottoprogetto 1).
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Gasparo, M.G., Macconi, M. Numerical solution of second-order nonlinear singularly perturbed boundary-value problems by initial-value methods. J Optim Theory Appl 73, 309–327 (1992). https://doi.org/10.1007/BF00940184
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DOI: https://doi.org/10.1007/BF00940184