DDA error analysis using sampled data techniques

Abstract

Sampled data techniques were first applied to digital operations by Linvill and Saltzer in order to study the errors resulting from the use of numerical integration techniques. The purpose of this paper is to develop an understanding for the mechanics of errors in the digital differential analyzer and to evolve a conceptually simple error theory. This is accomplished by establishing some of the basic comcepts regarding the applications of sampled data techniques to the integration process; developing the matrix model for the solution of a system of linear differential equations with constant coefficients on a digital differential analyzer and then using the W-transform to finalize the error theory. It is then easily shown that simple adjustments to the coefficient matrix of linear differential equations with constant coefficients will allow one to obtain solutions to these equations the accuracy of which is limited only by round-off errors.