Sextic spline solution for solving a fourth-order parabolic partial differential equation

Abstract

A fourth-order parabolic partial differential equation in one space variable which arises in the study of transverse vibrations of a uniform flexible beam is solved. The numerical solution is obtained by using a new three-level method based on a sextic spline in space and finite-difference discretization in time. Stability analysis of the method has been carried out. It is shown that we obtain a scheme of O(k 2+h 4) and O(h 4+h 2 k 2). The method is tested on a problem which has appeared in physical applications. Comparison with some known methods shows the superiority of the present method.