Multidimensional digital filter approach for numerical solution of a class of PDEs of the propagating wave type

Abstract

Numerical schemes exploiting passive multidimensional digital filtering methods for the solution of partial differential equations describing a large variety of physical systems are studied. We consider a system of linear differential equations in (n+1) variables that model a variety of physical phenomena. The technique involves mapping the PDEs into a (n+1) dimensional passive digital filter essentially via a rotation of the space-time coordinates. The passive digital filter is then synthesized by means of internally or structurally passive building blocks. Similar solutions have been proposed in the very recent past using wave digital filter principles. While this technique relies heavily on the formalism of classical analog network theory, our method is more akin to the so called orthogonal filter principle, and is believed to be more direct without having to explicitly use any result from the synthesis theory of classical networks.