Exponentially convergent symbolic algorithm of the functional-discrete method for the fourth order Sturm–Liouville problems with polynomial coefficients

Abstract

A new symbolic algorithmic implementation of the functional-discrete (FD-) method is developed and justified for the solution of fourth order Sturm-Liouville problem on a finite interval in the Hilbert space. The eigenvalue problem for the fourth order ordinary differential equation with polynomial coefficients is investigated. The sufficient conditions of an exponential conver-* sults. The numerical results obtained with the FD-method are compared with the numerical test results obtained with other existing numerical techniques.