A class of difference scheme for solving telegraph equation by new non-polynomial spline methods

In this paper, by using a new non-polynomial parameters cubic spline in space direction and compact finite difference in time direction, we get a class of new high accuracy scheme of O(τ4 + h2) and O(τ4 + h4) for solving telegraph equation if we suitably choose the cubic spline parameters. Meanwhile, stability condition of the difference scheme has been carried out. Finally, numerical examples are used to illustrate the efficiency of the new difference scheme.