The thesis describes the design of a digital computer system which can provide the precision of digital techniques, with the speed of analogue processing together with the flexibility of the hybrid computer. The application of Digital Differential Analyser (DDA) techniques is discussed and two forms of DDA are described. The first (SOIC I) embodies several improvements on previously applied techniques. These include a programmable electronic patching system, a one step integration algorithm, coefficient potentiometers and a method of implementing a suggestion of McGhee and Nilsen. The second machine (SOIC II) uses an original form of digital integrator and consists of 64 computing elements which are interconnected by a programmable logic sy...