Abstract
This Thesis which is submitted for the Higher Degree of Doctor of Philosophy is concerned with research into the Matrix Digital Differential Analyser (M. D. D. A. ) which was carried out in the period October 1972 to October 1976. An introduction to Digital Differential Analyser (D. D. A. ) is given using the results of a liturative search in chapter one. The developmental history of the D. D. A. from its beginnings in the early 1950's to the present day is covered. This is followed by a chapter on the Extention of Incremental Techniques to Matrices. A mathematical justification is given for the operations performed on Matrices by the M. D. D. A. The integration algorithms as applied to Matrices are also dealt with. Using this information a Matrix Digital Differential Analyser was postulated. Simulations were carried out using a General Purpose Computer to check the performance of the M. D. D. A. integration algorithm. Chapter three describes the design of the M. D. D. A. It was designed to demonstrate the feasability of constructing an M. D. D. A. whilst keeping system complexity as low as possible. The overall system as well as the paper tape interface is also described. The detailed design and construction of the M. D. D. A. Integrator is covered in Chapter four. Subsystems which comprise the Integrator have their overall design and operation described. Similarly chapters five and six do the same for the M. D. D. A Multiplier and M. D. D. A. Output unit. The use of an M. D. D. A. to solve Linear Differential Equations is illustrated in chapter seven. A method of problem scaling is described using an example and also a way of solving Simultaneous Linear Differential Equations. Chapter eight is the results chapter, the solutions to a number of well known Linear Differential Equations obtained using the M. D. D. A. are compared with the analytic solutions The results are then analysed and the solution accuracy considered. A final chapter is then used to consider a number of the limitations of the structure of the current M. D. D. A. , and to suggest improvements which would lead to a M. D. D. A. with a superior performance.