Numerical methods for computing the eigenvalues of linear fourth-order boundary-value problems

AbstractNovel finite-difference methods are developed for approximating the eigenvalues of three types of linear, fourth-order, two-point, boundary-value problems. The fourth-order differential equation is transformed into a system of first-order equations and the numerical methods are derived by replacing the matrix exponential function in a recurrence relation by Padé approximants. Numerical results are obtained for a number of problems from the literature