The Extended Resolution Digital Differential Analyzer: A New Computing Structure for Solving Differential Equations

TLDR: It is shown that DDA speed and accuracy can be greatly improved by using increment word lengths which are approximately one-half the length of integrand registers providing that integration formulas more accurate than Euler integration are used.

Abstract: In conventional digital differential analyzers (DDA), the word length used for the transmission of information between integrators is restricted to at most a single magnitude bit and a sign bit. This restriction seriously limits integrator frequency response and has to a large extent been responsible for the failure of DDAs to achieve widespread acceptance as general purpose differential analyzers. In this paper it is shown that DDA speed and accuracy can be greatly improved by using increment word lengths which are approximately one-half the length of integrand registers providing that integration formulas more accurate than Euler integration are used. The programming of such machines for the solution of both linear and nonlinear differential equations is discussed and a quantitative evaluation of performance improvement is presented. At the same time, an effort is made to isolate the principal difficulties in hardware implementation which result from extending the integrator increment resolution.