Spline methods for the solutions of hyperbolic equations

Second-order hyperbolic equations with mixed boundary conditions are solved, by using a non-polynomial cubic spline in space and finite difference in time direction. We develop new classes of three level methods. Stability analysis of the methods have been carried out. It has been shown that by suitably choosing the cubic spline parameters most of the previous known methods for homogeneous and non-homogeneous cases can be derived from our methods. We also obtain new high accuracy schemes of O(k2+h2)O(k2+h2) and O(k2+h4)O(k2+h4). Numerical example is given to illustrate the applicability and efficiency of the new methods.