The following are some Julia packages for scientific computing where I have been quite involved.
IntervalArithmetic.jl: Rigorous floating-point calculations using interval arithmetic in Julia. D.P. Sanders and L. Benet [doi]
IntervalRootFinding.jl: Find all roots of a function in a guaranteed way with Julia. D.P. Sanders and L. Benet
ReachabilityAnalysis.jl: Reachability Computations for Dynamical Systems in Julia. M Forets, C. Schilling, D. Freire Caporale, D.P. Sanders, L. Benet and S. Guadalupe
TaylorIntegration.jl: ODE integration using Taylor's method, and more, in Julia. J.A. Pérez-Hernández and L. Benet [doi]
TaylorModels.jl: Rigorous function approximation using Taylor models in Julia. L. Benet and D.P. Sanders [doi]
TaylorSeries.jl: A Julia package for Taylor polynomial expansions in one and several independent variables. L. Benet and D.P. Sanders [doi]
ValidatedNumerics.jl: Umbrela package for rigorous floating-point calculations with interval arithmetic in Julia. D.P. Sanders and L. Benet [doi]
See also JuliaIntervals and JuliaReach web pages.