Non-Stationary Subdivision for Inhomogeneous Order Differential Equations

This paper provides a methodology for the systematic derivation of subdivision schemes that model solutions to inhomogeneous order linear differential equations. In previous work, we showed that subdivision can be used to capture very efficiently the solutions of homogeneous order, linear differential equations. The resulting subdivision masks are stationary and can be precomputed, allowing for very simple and fast application of these schemes. In this paper, we show that this method can be extended to express solutions of systems of inhomogeneous order, linear differential equations. Even though the resulting subdivision masks may be non-stationary, the masks can again be precomputed. Thus, the resulting subdivision schemes capture very efficiently solutions of inhomegeneous order, linear partial differential equations.