抄録
D.D.A. (Digital Differential Analyzer) has a useful high performance for many applications, especially for numerical control. It can, for example, generate any outline curves of a part by concatinating solution curves of various differential equations.
Owing to several reasons, however, the D.D.A. 's high performance has never been fully utilized in practice. One of the most serious of these reasons is the difficulty in estimating accurately the error in D.D.A. computation.
This paper presents a new and generalized method of computation error analysis in solving any ordinary linear differential equations with constant coefficients. In this method, each digital integrator is replaced equivalently by an ideal analogue integrator with an error function E(t) added to its output. Then, the computation error is obtained as a solution of a linear differential equation having some forcing function. An explicit representation of the computation error is given, from which the upper and lower bounds of the computation error can be estimated by easy calculations.
Some examples show that such estimation of error is sufficiently accurate and useful for many applications of D.D.A.
One of the most important results of this paper is that the computation error in solving a linear differential equation decreases proportionally with the size of the unit increment in the digital integration. From this fact it is shown that any linear differential equation can be solved with the computation error of at most one unit of increment by a special programming.
