Sextic spline solution of variable coefficient fourth-order parabolic equations

Abstract

We report new three-level implicit methods of O(k ²+h ⁴) and O(k ⁴+h ⁴) for the numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficients. We use sextic spline in space and finite difference in time directions. Sextic spline function relations are derived by using off-step points. The linear stability of the presented method is investigated. We solve test problems numerically to validate the derived methods. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords:

• beam vibration
• fourth-order parabolic equation
• sextic spline
• stability analysis
• convergence
• variable coefficient

C.R. Category :

• G.1.8