On the eigenvalue problem on a semi infinite interval

In this paper, we are concerned with the solution of a class of boundary value problems − y ″ + f ( x ) y = λ y , 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 i v ( x ) | is bounded. The theory is applied to compute the eigenvalues when f ( x ) = x 2 for which explicit solutions are known.