Abstract :
The behaviour of a linear servo-mechanism may be described by a set of linear first-order simultaneous differential equations. The programme applies, however, to other problems that can be described similarly and to partial differential equations which can be reduced to this form by finite-difference approximations. The digital differential analyser and similar analogue devices are considered, but a general-purpose machine is more versatile. A form of Runge-Kutta formula for the numerical integration of the equations is described. Each coefficient in the set of equations may be described by a code word which specifies both its magnitude and location. An interpretation routine examines these code words in turn and evaluates the derivatives required in the integration formula. The solution for any variable may be punched out or displayed on a cathode-ray tube, and parameters are easily varied when searching for an optimum design. By adding suitable sub-routines the general programme is easily adapted to handle non-linear systems. The technique is most useful for supplementing preliminary studies on a simple analogue computer and is more adaptable for non-linear systems. A simple worked example is used to illustrate the principles without assuming previous experience of either numerical analysis or computing machines.
