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Based on the prior error bound and the mesh equidistribution principle, it is proved that there exists a mesh gives optimal first-order convergence which is robust with respect to the perturbation parameter. Finally, the posterior error bound is used to choose a suitable monitor function and design a corresponding adaptive grid generation algorithm. Numerical results are given to illustrate our theoretical result.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023044","type":"journal-article","created":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T00:27:00Z","timestamp":1679531220000},"page":"1006-1023","source":"Crossref","is-referenced-by-count":4,"title":["A robust adaptive grid method for first-order nonlinear singularly perturbed Fredholm integro-differential equations"],"prefix":"10.3934","volume":"18","author":[{"given":"Zhi","family":"Mao","sequence":"first","affiliation":[{"name":"School of Data Science, Tongren University, Tongren 554300, China"},{"name":"School of Mathematics and Statistics, Jishou University, Xiangxi 416100, China"}]},{"given":"Dan","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Jishou University, Xiangxi 416100, China"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023044-1","unstructured":"D. O'Regan, M. 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