doi:10.1002/mma.8446engGracia Lozano, J. L.Navas-Montilla, A.O''Riordan, E.Parameter-uniform numerical methods for singularly perturbed linear transport problemsART-2022-129573Pointwise accurate numerical methods are constructed and analysed for three classes of singularly perturbed first order transport problems. The methods involve piecewise-uniform Shishkin meshes and the numerical approximations are shown to be parameter-uniformly convergent in the maximum norm. A transport problem from the modelling of fluid–particle interaction is formulated and used as a test problem for these numerical methods. Numerical results are presented to illustrate the performance of the numerical methods and to confirm the theoretical error bounds established in the paper. © 2022 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons, Ltd.2022http://zaguan.unizar.es/record/11818610.1002/mma.8446http://zaguan.unizar.es/record/118186oai:zaguan.unizar.es:118186info:eu-repo/grantAgreement/ES/DGA-FEDER/E24-17Rinfo:eu-repo/grantAgreement/ES/MICINN-FEDER/PGC2018-094341-B-I00info:eu-repo/grantAgreement/ES/MICINN PID2019-105979GB-I00Mathematical Methods in the Applied Sciences (2022), 8446 [22 p.]by-nc-sahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccess