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Software based on explicit RK formulas. (English) Zbl 0868.65043
The authors give their personal view on the development which has taken place in explicit Runge-Kutta (RK) methods during the last three decades. Some of the aspects discussed are: Choice of step size, global error assessment, how to detect stiffness, continuous extension of the solution and evaluation of methods and implementations. They finish the article by listing a number of topics which still remain to be investigated.
MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
65-03 History of numerical analysis
01A65 Development of contemporary mathematics
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