The Serial Solution of the Diffusion Equation Using Non-Standard Hybrid Techniques

摘要

In the conventional approach to the serial solution of the one-dimensional diffusion equation using continuous space-discrete time (CSDT) techniques, there is a large amount of positive feedback in the resultant analog programming. For all practical purposes, the presence of this positive feedback makes the conventional analog method useless. In this paper, a new direction of attack is proposed, utilizing the equivalence between the ordinary differential equation and the corresponding integral equation. The application of this technique to two demonstration problems, though relatively simple ones, is entirely satisfactory. Furthermore, the method demonstrated here can be applied to situations where the coefficient of the diffusion equation is a spatial function. At the end of the report, a brief discussion is also given on possible modifications to the technique used, so as to shorten the solution time. (Author)