Asymptotic correction of Numerovʹs eigenvalue estimates with natural boundary conditions

Asymptotic correction, at negligible extra cost, greatly improves the accuracy of higher eigenvalues computed by finite difference or finite element methods, and generally increases the accuracy of the lower ones as well. This paper gives a brief overview of the technique and describes how its previous use with Numerovʹs method may be extended to problems with natural boundary conditions. Numerical results indicate that it is just as successful as with Dirichlet boundary conditions.