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Bill Gear describes the development of numerical methods for ordinary differential equations (ODE), beginning with a summary of the pre-automatic computing era. By the late the early 40's digital differential analyzers were in use and special purpose digital machines continued to be developed after the introduction of early electronic digital computers. The first implementations of numerical ODE solvers on the EDSAC and ILLIAC had to deal with small memory size. With the introduction of machines with larger memory sizes, the first adaptive codes were developed. Gear ends with a discussion of stiff ODEs and the development of codes to handle them.
Key words: digital differential analyzer, Mark I, Model III, fire control problems, ENIAC, special purpose digital machines, MADDIDA, EDSAC, ILLIAC, Runge-Kutta-Gill method, adaptive codes, Runge-Kutta-Gill method, variable order multistep code, stiff ODEs, backward differentiation formula, A-stability, A(a) stability, ODESSY, DIFSUB, chemical kinetics.
Funding Agency: U.S. Department of Energy
Time frame: 1940's, 1950's, 1960's
People: Howard Aitken, Stanley Gill, Gene Golub, David Wheeler, Arnold Nordsieck, Fred Krogh, C. F. Curtiss, J.O. Hirschfelder, Germund Dahlquist, Olof Widlund, C. W. Gear
Location: Harvard University, Bell Laboratories, Watson Scientific Computing Laboratory, Columbia University; University of Illinois, Argonne National Laboratory
Copyright: History of Scientific Computing, Stephen G. Nash, editor, ACM Press, Association for Computing Machinery, New York, 1990, pp 88-105. with permission