Recent Developments in Numerical Integration

Classical and even modern developments of numerical integration have not been directly concerned with the frequency-response of integration algorithms. The frequency-response characteristics of an integrator are usually presented only as a property of the integrator. When numerical integration is used in all digital (or hybrid) simulation, digital computer controlled systems or other discrete information systems, much care is given to selecting a numerical integration formula with well-behaved frequency-response characteristics. This paper is concerned with the development of a set of numerical integrators suited for application in information systems. These integrators are synthesized in such a way that they have well-defined frequency-response characteristics WHICH CAN BE VARIED; thus, each of these integrators can be tailored to integrate accurately and efficiently in many different applications. These methods of numerical integration have stability, accuracy, and noise-controlling parameters. Analytical and empirical methods of selecting the values of these parameters are discussed in detail.