100 years of the Runge-Kutta method: a brief editing for schools

Authors: Böckmann C.; Brückner A.

Source: Teaching Mathematics and its Applications, Volume 20, Number 1, 2001 , pp. 25-49(25)

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Abstract:

This paper reports on the historical development of the Runge-Kutta methods beginning with the simple Euler method up to an embedded 13-stage method. Moreover, the design and the use of those methods under error order, stability and computation time conditions is edited for students of numerical analysis at undergraduate level. The second part presents applications in natural sciences, compares different methods and illustrates some of the difficulties of numerical solutions.

Language: English

Document Type: Original article

Affiliations: E-mail: bockmann@rz.uni-potsdam.de Department of Numerical Mathematics, Institute of Mathematics, University of Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany

Publication date: 2001-01-01

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The journal provides a forum for the exchange of ideas and experiences which contribute to the improvement of mathematics teaching and learning for students from upper secondary/high school level through to university first degree level. A distinctive feature of the journal is its emphasis on the applications of mathematics and mathematical modelling within the context of mathematics education world-wide. The journal's readership consists of mathematics teachers, students, researchers and those concerned with curriculum development and assessment, indeed anyone concerned about the education of users of mathematics.