Transformation approach to numerically integrating PDEs by means of WDF principles (Q1176556)

The aim of the paper is to find the discrete passive dynamical system which allows to integrate given partial differential equation (PDE). The paper is a continuation of the work of the first author [Wave digital filters: theory and practice, Proc. IEEE, 74, 270-327 (1986)] where the method of wave digital filters was developed. The main novelty of the paper is an observation that for some PDE's a linear transformation of variables can be found such that the equation written in new coordinates is passive with respect to any coordinate (not only the time variable). Solution to such an equation can be represented as an output of certain electrical circuit with all elements passive. This ideas are applied in the paper to solving Maxwell's equations.