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The iterative differential analyzer utilizes both continuous and incremental or iterative mathematical techniques for the solution of problems. Consequently, this machine is frequently required to perform numerical integration. In this connection it is desirable to evaluate numerical integration techniques from a control system point of view. The W-trans-form, a special case of the modified Z-trans-form, is used as a base for analysis. The true numerical integration operator is shown to have the form T(logw) where T is the time increment for the process. The truncation error for an integration process is related to the dynamic error of the corresponding integration operator which is determined by comparison with T(logw). Various integration operators are evaluated with respect to dynamic error. Parasitic solutions are shown to correspond to poles of the W-transfer function of the operator. Round-off error accumulation may be determined from the W-plane representation of the operator. Synthesis of open-loop operators using root-locus and Bode techniques is discussed. Closed-loop operator selection and stability for the integration of linear ordinary differential equations is discussed. Techniques are indicated for the stabilization of closed-loop operators. Techniques are presented for the determination of truncation and round-off error estimates for the integration of linear ordinary differential equations.

The spectral evaluation of iterative differential analyzer integration techniques