The usual methods of the solution of partial differential equations require a lot of computing elements, but the number of computing elements may be reduced by employing time-sharing computation utilizing analog memory. The problem is presented here that it takes more computing time and that the memory error becomes a new source of error which increases the solution error. In this paper, the authors have taken up the equation of heat conduction as an example and calculated the speed of convergence and computing error in order to find standard values for this kind of problems, and then consider the appropriate number of division. Moreover, the authors have presented a new method of speeding up convergence and reducing error of time-sharing computation, and proved its effectiveness.