  This paper describes a new numerical method for solving eigenstate problems,
such as time-independent Schrodinger equation. The idea is to use the first
order perturbation theory to rewrite the eigenvalue problem as a system of
first order differential equations and then solve them using numerical
techniques. The method allows to introduce perturbation terms of any order of
magnitude. The algorithm is in some cases faster than conventional variational
method and offers a new insight into perturbation theory. It is also easy to
understand and implement.
