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The computation of the self-force constitutes one of the main challenges forthe construction of precise theoretical waveform templates in order to detectand analyze extreme-mass-ratio inspirals with the future space-basedgravitational-wave observatory LISA. Since the number of templates required isquite high, it is important to develop fast algorithms both for the computationof the self-force and the production of waveforms. In this article we show howto tune a recent time-domain technique for the computation of the self-force,what we call the Particle without Particle scheme, in order to make it veryprecise and at the same time very efficient. We also extend this technique inorder to allow for highly eccentric orbits.

Tuning Time-Domain Pseudospectral Computations of the Self-Force on a Charged Scalar Particle