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Numerical methods for ordinary differential equations in the 20th century. (English) Zbl 0969.65063

The paper is a survey following many of the main strands in the development of numerical methods for general initial value problems, stiff systems, or special problem types. The early contributions of Bashforth, Adams and Runge, together with an introduction to the fundamental work of Euler form the subject of a first section.
Further sections deal either with specific periods of time or with contributions with a unifying scheme: Heun, Nyström and Moulton papers, Milne’s device, Taylor series, modern theory of linear multistep methods and Runge-Kutta methods. Nontraditional methods are also revised.
A special section is dedicated to stiff problems, and another to the beginnings of differential equation software. The last section treats some special problems.

MSC:

65L05 Numerical methods for initial value problems involving ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
01A60 History of mathematics in the 20th century
65-03 History of numerical analysis
34A34 Nonlinear ordinary differential equations and systems

Software:

DASSL; DIFSUB
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Full Text: DOI

References:

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