Modeling and design of fiber lasers facilitate the process of their practical realization. Of particular interest during the last few years is the development of lanthanide ion-doped fiber lasers which operate at wavelengths exceeding 2000 nm. There are two main host glass materials considered for this purpose, namely fluoride and chalcogenide glasses. Therefore, this study concerns comparative modeling of fiber lasers operating within the infrared wavelength region beyond 2000 nm. In particular, the convergence properties of selected algorithms, implemented within various software environments, are studied with a specific focus on the central processing unit (CPU) time and calculation residual. Two representative fiber laser cavities are considered: one is based on a chalcogenide-selenide glass step-index fiber doped with trivalent dysprosium ions whilst the other is a fluoride step-index fiber doped with trivalent erbium ions. The practical calculation accuracy is also assessed by comparing directly the results obtained from the different models.