In this paper computational algorithms are presented to compute the eigenvalues of Schrodinger operators with definite and indefinite weights. The algorithms are based on Titchmarsh-Weyl's theory and can be applied to solve a wide class of problems in quantum mechanics. Explicit examples are presented, some of which recover the known exact solutions. Finally, some analytical bounds have been reviewed for definite and indefinite singular problems. Weyl's Spectral Bisection Algorithm has been proposed to solve definite problems as algebraic problems. Open problems have been presented based on the results of the presented algorithms.