The development of ODE methods: a symbiosis between hardware and numerical analysis

Abstract

The history of the numerical solution of ordinary differential equations is surveyed from its origins three centuries ago up to the early 1970s. The increasing demands for the solution of ODEs, especially for exterior ballistics and celestial mechanics, has been a primary stimulus of and a significant influence on the early development of computers starting with the analog differential analyzers and continuing to the first wired-program digital computers—whose form foreshadowed future developments in parallel computers. At the same time the hardware has, of course, affected the algorithms used, but this has resulted in surprisingly few innovations in numerical techniques.