Numerical integration of nonlinear multidimensional systems

The suitability of methods from multidimensional systems theory and digital signal processing for the efficient simulation of time and space dependent problems has already been demonstrated. Properly chosen functional transformations for the time and space coordinates turn a partial differential equation into a transfer function description of a multidimensional continuous system. It serves as the starting point for the derivation of a discrete system which closely models the behaviour of the given continuous system and which is suitable for computer implementation. This concept is extended here to the simulation of nonlinear multidimensional systems. The essence of the presented method is a systematic way to turn a nonlinear partial differential equation into a set of ordinary differential equations, for which standard methods for numerical integration exist. This paper briefly reviews the linear case, points out the various difficulties arising from nonlinearity and shows how to overcome them. Numerical results demonstrate the effectiveness of the method.