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.

Keywords:

• Fourth-order parabolic equation
• Sextic spline
• Spline relations
• Stability analysis
• Vibrating beam