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We present a systematically improvable method for numerically solvingrelativistic three-body integral equations for the partial-wave projectedamplitudes. The method consists of a discretization procedure in momentumspace, which approximates the continuum problem with a matrix equation. It issolved for different matrix sizes, and in the end, an extrapolation is employedto restore the continuum limit. Our technique is tested by solving a three-bodyproblem of scalar particles with an $S$ wave two-body bound state. We discusstwo methods of incorporating the pole contribution in the integral equations,both of them leading to agreement with previous results obtained usingfinite-volume spectra of the same theory. We provide an analytic and numericalestimate of the systematic errors. Although we focus on kinematics below thethree-particle threshold, we provide numerical evidence that the methodspresented allow for determination of amplitude above this threshold as well.

Solving relativistic three-body integral equations in the presence of bound states