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Runge-Kutta research at Toronto. (English) Zbl 0870.65063
Authors’ abstract: The main purpose of this paper is to review the work of 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 differential equations, but, with just a few exceptions, specific 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, differential-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 effectiveness, taking advantage of parallelism, and handling discontinuities, are also discussed.

MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
01A65 Development of contemporary mathematics
01A73 History of mathematics at specific universities
65-03 History of numerical analysis
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