Analogue solution of elliptic differential equations by conformal transformations

A new method is described for the simulation of distributed-parameter systems. Conformal transformations are used to convert the boundary-value problem to a set of initial-value problems capable of direct solution on an analogue computer. Since the equations involved are solved in parallel, the method provides a means for rapid online modelling. It is shown that the simultaneous solution of more than one transformation equation requires the use of generalised integrators. Some preliminary results on a heat-flow problem are included to illustrate the application of the technique and to confirm its validity. The computing accuracy is shown to compare very favourably with existing alternative methods, with the added advantage that the new method is relatively insensitive to noise products.