An Electronic Differential Analyzer

An electronic differential analyzer is described, capable of solving ordinary differential equations of orders through the sixth, both linear and nonlinear, and with coefficients that are either constant or variable. This analyzer has a high speed of operation and is extremely flexible with regard to equation parameters and initial conditions. The flexibility permits rapid investigation of wide ranges of equation solutions with regard to periodicity, instability, and discontinuities. It renders practicable the solution of end-point boundary-value problems; that is, problems in which the final rather than initial values are specified. Two new computing elements, an electronic function generator and an electronic multiplier, are employed in this differential analyzer. A diode clamping circuit permits the use of ac coupled amplifiers. A number of representative differential equations of the linear and nonlinear types have been solved. Comparison of observed and calculated solutions reveals an accuracy of from 1 to 5 per cent, while the precision (or repeatability) of the solutions ranges from 0.002 to 0.1 per cent. An analysis of the errors introduced into the differential-equation solutions by the frequency limitations of the computing elements, such as the integrators and adders, has been made, and the results of this analysis have been verified experimentally.