On the eigenvalue problem on a semi infinite interval (original) (raw)

In this paper, we are concerned with the solution of a class of boundary value problems −y + f (x)y = λy, y(0) = 0, y(∞) = 0, where f (x) monotonically increases to infinity as n increases to infinity. We use finite difference scheme to reduce the system to an equivalent system of an infinite linear algebraic eigenvalue problem. We give a precise error analysis for the eigenvalues of the approximate system and an error analysis for the continuous system under the condition that |y iv (x)| is bounded. The theory is applied to compute the eigenvalues when f (x) = x 2 for which explicit solutions are known.