{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:17:29Z","timestamp":1776784649401,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"252","license":[{"start":{"date-parts":[[2006,6,7]],"date-time":"2006-06-07T00:00:00Z","timestamp":1149638400000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>In this paper singularly perturbed semilinear differential equations with a discontinuous source term are examined. A numerical method is constructed for these problems which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented that validate the theoretical results.<\/p>","DOI":"10.1090\/s0025-5718-05-01764-3","type":"journal-article","created":{"date-parts":[[2005,8,10]],"date-time":"2005-08-10T10:23:21Z","timestamp":1123669401000},"page":"1759-1776","source":"Crossref","is-referenced-by-count":25,"title":["A class of singularly perturbed semilinear differential equations with interior layers"],"prefix":"10.1090","volume":"74","author":[{"given":"P.","family":"Farrell","sequence":"first","affiliation":[]},{"given":"E.","family":"O\u2019Riordan","sequence":"additional","affiliation":[]},{"given":"G.","family":"Shishkin","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2005,6,7]]},"reference":[{"key":"1","series-title":"Applied Mathematical Sciences","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1114-3","volume-title":"Nonlinear singular perturbation phenomena: theory and applications","volume":"56","author":"Chang, K. 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Shishkin, Singularly perturbed differential equations with discontinuous source terms, Proceedings of \u201cAnalytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems\", Lozenetz, Bulgaria, 1998, J.J.H. Miller, G. I. Shishkin and L.Vulkov eds., Nova Science Publishers, Inc., New York, USA, 23\u201332, 2000."},{"key":"8","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1142\/2933","volume-title":"Fitted numerical methods for singular perturbation problems","author":"Miller, J. J. H.","year":"1996","ISBN":"https:\/\/id.crossref.org\/isbn\/9810224621"},{"key":"9","unstructured":"J. J. H. Miller, E. O\u2019Riordan and G. I. Shishkin, Fitted mesh methods for the singularly perturbed reaction diffusion problem, In Proc. of V-th International Colloquium on Numerical Analysis, Aug. 13-17, 1996, Plovdiv, Bulgaria, Academic Publications, ed. E. 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I.","year":"1991","journal-title":"Soviet J. Numer. Anal. Math. Modelling","ISSN":"https:\/\/id.crossref.org\/issn\/0169-2895","issn-type":"print"},{"key":"13","unstructured":"G. I. Shishkin, Discrete approximation of singularly perturbed elliptic and parabolic equations, Russian Academy of Sciences, Ural section, Ekaterinburg, (1992). (in Russian)"},{"issue":"215","key":"14","doi-asserted-by":"publisher","first-page":"1085","DOI":"10.1090\/S0025-5718-96-00753-3","article-title":"A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions","volume":"65","author":"Sun, Guang Fu","year":"1996","journal-title":"Math. 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