  We propose a solution method for studying relativistic spin-$0$ particles. We
adopt the Feshbach-Villars formalism of the Klein-Gordon equation and express
the formalism in an integral equation form. The integral equation is
represented in the Coulomb-Sturmian basis. The corresponding Green's operator
with Coulomb and linear confinement potential can be calculated as a matrix
continued fraction. We consider Coulomb plus short range vector potential for
bound and resonant states and linear confining scalar potentials for bound
states. The continued fraction is naturally divergent at resonant state
energies, but we made it convergent by an appropriate analytic continuation.
