A New Two Level Difference Scheme for Solving One-Dimensional Second-Order Hyperbolic Equations

In this paper, a new numerical method is developed for solving one-dimensional second-order hyperbolic equations. By using a new unconditionally stable two level difference scheme based on the quartic spline interpolation method in space direction and generalized trapezoidal formula in time direction, the hyperbolic equations are solved. Stability analysis of the scheme is carried out. The accuracy of the scheme is second-order in time direction and fourth-order in space direction. It has been shown that by suitably choosing parameter, a high accuracy scheme of third-order accurate in time direction can be derived from the method. Numerical results comparison demonstrate the superiority of the new scheme.