Non-polynomial quartic spline methods for the solution of the equation of vibrating rod

In this paper, we employ a new three level implicit methods based on non-polynomial quartic spline for numerical solution of fourth-order homogeneous parabolic partial differential equation by using off-step points. By using non-polynomial quartic spline in space and finite difference in time directions, we obtain various im- plicit three level methods. Stability analysis of the presented methods have been carried out. We solve two test problems numerically to validate the proposed derived methods. Numerical comparison with other existence methods shows the superiority of our presented schemes.