A modified difference and a Numerov-like scheme have been introduced i
n a shooting algorithm for the determination of the (higher-lying) eig
envalues of Schrodinger equations and Sturm-Liouville problems. Some n
umerical experiments are introduced. Time measurements have been perfo
rmed. The proposed algorithms are compared with other previously intro
duced shooting schemes. The structure of the eigenvalue error is discu
ssed.