The introduction of dynamic errors in the solutions of linear differential equations by electronic analog computers has been given considerable attention. The previous work on the subject is reviewed herein and a useful application of these results is illustrated. The presentation of the error data is given in terms of the shift in the characteristic roots of the equation caused by the limited bandwidths of the operational amplifiers. A graphical representation, useful in predicting the bounds on the root shift, is also illustrated. Although the example shown is based on a linear second-order differential equation, it is observed that the method can be extended to higher-order linear characteristic equations.

The use of controlled superconductors in analog-computer circuitry is discussed. It is shown that the operations of summation, multiplication by a constant, differentiation, integration, and multiplication of two variables may be performed by these circuits. It is pointed out that the advantages of compactness, reliability, and light weight that are inherent to the use of controlled superconductors are now obtainable for analog as well as for digital equipment.

Due to the physical unrealizability of electronic adding and integrating circuits with ideal characteristics, errors will be introduced in the solution of differential equations obtained by the use of electrical analog computers. Numerical errors in the solution will be introduced by fluctuations in the value of plate and of grid supply voltages, changes in the values of circuit components, and changes in the values of the vacuum tube constants. In addition, the limited frequency response of the machine components will cause the computer to solve a characteristic equation of a higher order than the original characteristic equation whose solution is desired. The error in the solution manifests itself as a shifting in the roots of the original characteristic equation as well as the production of some extra roots. The effect of this change in the root position as well as the presence of the extra roots is experienced in the curve of the solution as a function of the independent variable. In a paper on the accuracy of differential analyzers, Macnee1 has derived an expression which gives the value of the characteristic root shift. The use of this expression is accurate only for certain types of ordinary differential equations. In this paper a new expression for the value of the root shift is derived. The analysis preceding the new root-shift expression is developed in such a manner as to include the Macnee analysis as a special case.