A semi-discretization method based on quartic splines for solving one-space-dimensional hyperbolic equations

In this paper, based on C³ quartic splines, a semi-discretization method containing two schemes is constructed to solve one-space-dimensional linear hyperbolic equations. It is shown that both schemes are unconditionally stable and their approximation orders are of O(k⁵+h⁴) and of O(k⁷+h⁴) with k and h being step sizes in time and space, respectively, which are much higher than those of other published schemes. A numerical example is presented and the results are compared with other published numerical results.