Runge - Kutta Research at Toronto ?
نویسنده
چکیده
The main purpose of this paper is to review the work on Runge-Kutta methods at the University of Toronto during the period 1963 to the present (1996). To provide some background, brief mention is also made of related work on the numerical solution of ordinary diierential equations, but, with just a few exceptions, speciic references are given only if the referenced material has a direct bearing on Runge-Kutta methods and their application to a variety of problem areas. There are several main themes. New Runge-Kutta formulas and new error control strategies are developed, leading for example to continuous methods and their application to areas such as delay, diierential-algebraic and boundary-value problems. Software design and implementation are also emphasized. And so is the importance of careful testing and comparing. Other topics, such as the notion of eeectiveness, taking advantage of parallelism, and handling discontinuities, are also discussed. 1 A brief prehistory Interest in Runge-Kutta methods was aroused for Hull at the University of British Columbia after the arrival in 1957 of UBC's rst computer, an Alwac III E with an 8K word drum memory but with practically no software beyond a few elementary function routines and a program to play Tic-Tac-Toe. (Early on, a potentially worrisome event took place: the Dean with nancial responsibility for the new Computing Centre suuered a humiliating defeat by the program on his rst visit to the Centre.) ?
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