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(2008)

Towards Digital Mathematics Library. Birmingham, United Kingdom, July 27th, 2008

The convergence of explicit Runge-Kutta methods combined with Richardson extrapolation

Faragó, István, Havasi, Ágnes, Zlatev, Zahari (2012)

Applications of Mathematics 2012

Runge-Kutta methods are widely used in the solution of systems of ordinary differential equations. Richardson extrapolation is an efficient tool to enhance the accuracy of time integration schemes. In this paper we investigate the convergence of the combination of any explicit Runge-Kutta method with active Richardson extrapolation and show that the obtained numerical solution converges under rather natural conditions.

The Impact of Modern Mathematics on Ancient Mathematics

Wilbur R. Knorr (2001)

Revue d'histoire des mathématiques

In a hitherto unpublished lecture, delivered in Atlanta, 1975, W.R. Knorr reflects on historical method, its sensitivity to modern work, both in mathematics and in the philosophy of mathematics. Three examples taken from the work of Tannery, Hasse, Scholz and Becker and concerning the study of pre-euclidean geometry are discussed: the mis-described discovery of irrational ‘numbers’, the alleged foundations crisis in the 5th century B.C. and the problem of constructibility.

The problems of definition

Jean-Pierre Ginisti (1991)

Mathématiques et Sciences Humaines

The aim of this paper is to present the great kinds of definitions known in mathematical logic, their goals and their means, from their historical and philosophical background (notably thanks to the proof of two theorems), and in order to situate, within this field, the others contributions which make up this number.

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