TWO-DIMENSIONAL STATE SPACE MODEL FOR PARTIAL DIFFERENTIAL EQUATIONS AND ITS SOLUTION

摘要

In this paper, Multi-Dimensional (M-D) state space model has been used to represent Partial Differential Equations (PDE). Several Models have been proposed for characterizing M-D maps. All models have an obvious iterative characteristic and show a quarter plane causal property. The models can be transformed to each other, so without loss of generality Fornasini-Marchesini (P.M.) model is considered as a description of a PDE and its solution is obtained. However, once the analysis for 2-D is done, the conceptual extension of methods to M-D is not difficult. As an example a wave equation is solved with different methods and results are compared with the multi-dimensional system approach. It is shown that multi-dimensional approach gives competitive results with other methods.