Numerical Methods Based on Non-Polynomial Sextic Spline for Solution of Variable Coefficient Fourth-Order Wave Equations

Abstract

A new technique based on non-polynomial sextic spline functions connecting spline functions values at mid knots and their corresponding values of the fourth-order derivatives is developed. We derive various classes of three level implicit spline methods for solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. These new numerical methods are based on non-polynomial sextic spline in space and finite difference in time directions. The linear stability of the presented methods is investigated. We solve test problems numerically to validate the derived methods. Numerical comparison with other existing methods shows the superiority of our presented scheme.

Keywords:

• Euler-Bernoulli beam equation
• non-polynomial sextic spline
• off-step points
• stability analysis
• convergence