Selected generalized integration techniques for analog computation

Abstract

Generalized integration is a technique for generating ex plicit functions on an analog computer by solving the appropriate differential equations they satisfy. Setting up the solution of differential equations using the parametric technique is first reviewed. Two theorems regarding the capability of linear equipment in generating sums and products are stated, and their usefulness is illustrated with examples. Applications of the technique to generating high-degree oscillatory polynomials and rational functions (which require nonlinear equipment) are also described. The major advantage of the technique is achievement of great accuracy with minimum equipment in some cases. The major disadvantage is that, with time, errors may sometimes increase and may not be bounded.