Quartic spline methods for solving one-dimensional telegraphic equations

In this paper, by using a quartic spline in space and generalized trapezoidal formula in time direction, one-dimensional telegraphic equations are solved. We present new classes of two-level schemes. The accuracy of these methods are O(k2+h4)O(k2+h4). It has been shown that by suitably choosing parameter, a high accuracy scheme of O(k3+h4)O(k3+h4) can be derived from our methods. Numerical results demonstrate the superiority of the new scheme.