On the eigenvalue problem −y″+f(x)y=λy−y″+f(x)y=λy 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=λy−y″+f(x)y=λy, y(0)=0y(0)=0, y(∞)=0y(∞)=0, where f(x)f(x) monotonically increases to infinity as nn 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 |yiv(x)||yiv(x)| is bounded. The theory is applied to compute the eigenvalues when f(x)=x2f(x)=x2 for which explicit solutions are known.