Arbitrary-order numerical schemes for linear hyperbolic systems

Abstract

This report is an extension of the work carried out in [16]. In [16] we defined arbitrary-order numerical methods for model scalar hyperbolic equation. In this report we extended these methods to linear hyperbolic systems where waves can propagate in both directions. First, we define a generalized numerical formula which can accommodate arbitrary wave speeds for scalar advection equation. Then to illustrate its application, we derive three, four, and five point generalization numerical schemes. Finally, according to the theory of linear systems, we extend the generalized schemes to linear hyperbolic systems in a straight forward manner.