Some new finite difference methods for computing eigenvalues of two-point boundary-value problems

AbstractThis brief note describes some new finite difference methods of order 2 and 3 for approximating eigenvalues of a two point boundary-value problem involving the differential equation y″ + (λq(x) − p(x))y = 0. These methods are based on the central difference formula h2y″i = δ2−112δ4 + 190δ6 − 1560δ8 + ⋯yi. Numerical results are tabulated in order to demonstrate practical usefulness of our methods