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We revisit the problem of calculating the quasinormal modes of spin $0$,$1/2$, $1$, $3/2$, $2$, and spin $5/2$ fields in the asymptotically flatSchwarzschild black hole spacetime. Our aim is to investigate the problem fromthe numerical point of view, by comparing some numerical methods available inthe literature and still not applied for solving the eigenvalue problemsarising from the perturbation equations in the Schwarzschild black holespacetime. We focus on the pseudo-spectral and the asymptotic iterationmethods. These numerical methods are tested against the available results inthe literature, and confronting the precision between each other. Besidestesting the different numerical methods, we calculate higher overtonesquasinormal frequencies for all the investigated perturbation fields incomparison with the known results. In particular, we obtain purely imaginaryfrequencies for spin $1/2$ and $3/2$ fields that are in agreement with analyticresults reported previously in the literature. The purely imaginary frequenciesfor the spin $1/2$ field are exactly the same as the frequencies obtained forthe spin $3/2$ field. In turn, the quasinormal frequencies for the spin $5/2$perturbation field are calculated for the very first time, and purely imaginaryfrequencies are found also in this case. We conclude that both methods provideaccurate results and they complement each other.

Revisiting the quasinormal modes of the Schwarzschild black hole: Numerical analysis