We investigate the behavior of several spatial grid methods and complex absorbers for strong-field and attosecond scenarios when using the time-dependent configuration-interaction singles method to solve the multielectron time-dependent Schrödinger equation for atoms. We compare the pseudospectral grid, finite-element, and finite-element-discrete-variable-representation (DVR) methods with each other and discuss their advantages and disadvantages. Additionally, we study the performances of complex absorbing potential (CAP) and smooth exterior complex scaling (SES) to absorb the outgoing electron. We find that SES performs generally better than CAP for calculating high-harmonic generation spectra and XUV photoelectron spectra. In both of these cases, the DVR and even more the FEM grid representations show more reliable results-especially when using SES. Both absorbers show drawbacks when calculating photoelectron spectra in the strong-field regime.