Erwin Fehlberg

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Erwin Fehlberg (born September 8, 1911 in Berlin-Oberschöneweide , † November 1990 in Huntsville ) was a German mathematician.

His most important merit is the development of step size controls for Runge-Kutta methods for the numerical solution of ordinary differential equations (thus today Runge-Kutta-Fehlberg method ).

life and work

After graduating from high school, he studied from 1930 at the university and the Technical University of Berlin (TH, today TU Berlin ) to become a teacher and in 1936 took the state examination in mathematics, physics and chemistry.

Only working as an aerodynamicist in the aircraft industry, Fehlberg began working in the Heereswaffenamt in Berlin in 1937 on practical and theoretical questions of external ballistics. In addition, he was a guest student at the Mathematical Seminar of the Institute for Applied Mathematics with Werner Schmeidler . In 1942, Fehlberg received his doctorate from Schmeidler with calculations on the displacement of the explosive point when shooting against air targets caused by ballistic-atmospheric disturbances.

After the war, Fehlberg developed numerical solution methods for ordinary differential equations, first in Frankfurt am Main (Germany), then in Drummondville (Canada). Since 1956 at the latest, Fehlberg has been working in a research laboratory at the Redstone Arsenal in Huntsville, Alabama, USA, which was incorporated into the Marshall Space Flight Center in 1960 .

In the following years, Erwin Fehlberg developed classic Runge-Kutta formula pairs of neighboring orders, e.g. B. 4th and 5th order as an approximation. The formulas of the higher order result from all formulas of the lower order as well as from only one or two other terms and thus require little additional computational effort. The individual formulas for each order give different results for the function sought. Their difference represents the numerical error ( local termination error ), which in turn is used to determine the next step size. Fehlberg's Runge-Kutta formula pairs result in particularly small errors, so that with the same accuracy requirement, larger step sizes result than with other methods of the same order. In addition to methods for solving ordinary first-order differential equations, Fehlberg also developed methods for second-order equations. The solution methods of the Runge-Kutta type constructed by Fehlberg are now known as the Runge-Kutta-Fehlberg method.

In 1969 Erwin Fehlberg received among others the “Exceptional Scientific Achievement Medal” from NASA.

literature

  • Renate Tobies : Biographical encyclopedia in mathematics for doctoral students at German universities and technical colleges, WS 1907/08 to WS 1944/45 . E. Rauner, Augsburg 2006, ISBN 3-936905-21-5 , pp. 101 .

Individual evidence

  1. ↑ Erwin Fehlberg: Remarks on the development of given functions according to Legendre's polynomials with application to the numerical integration of ordinary linear differential equations . In: Z. angew. Math. Mech . tape 31 , no. 4-5 , 1951, pp. 104–114 , doi : 10.1002 / zamm.19510310403 .
  2. ↑ Erwin Fehlberg: Remarks on the numerical treatment of Dirichlet's problem for more general margins . In: Acta Mathematica . tape 91 , no. 1 , December 1954, p. 51-74 , doi : 10.1007 / BF02393425 .
  3. ^ Erwin Fehlberg: A Numerical Solution of Boundary Value Problems for Nonlinear Ordinary Differential Equations. In: Transactions of the second Conference of Arsenal Mathematicians (held at the Ballistic Research Laboratories February 24, 1956) . Report No. 57-2. Office of Ordnance Research, Durham, North Carolina July 1957, pp. 1-7 .
  4. ↑ Dr E. Fehlberg: Classical Runge-Kutta formulas of the fifth and seventh order with step size control . In: Computing . tape 4 , no. 2 , June 1969, p. 93-106 , doi : 10.1007 / BF02234758 .
  5. ↑ Dr E. Fehlberg: Classical Runge-Kutta formulas of the fourth and lower order with step size control and their application to heat conduction problems . In: Computing . tape 6 , no. 1-2 , March 1970, pp. 61-71 , doi : 10.1007 / BF02241732 .
  6. ↑ Erwin Fehlberg, Siegfried Filippi, Josef Gräf: A Runge-Kutta-Nyström formula pair of order 10 (11) for differential equations of the form y '' = f (x, y) . In: Z. angew. Math. Mech . tape 66 , no. 7 , 1986, pp. 265-270 .
  7. ↑ Richard L. Burden, J. Douglas Faires: Numerical Analysis . 9th edition. Brooks Cole Publ., Pacific Grove 2010, ISBN 978-0-538-73564-3 , pp. 296-302 .
  8. ↑ J. Stoer, R. Bulirsch: Numerical Mathematics 2 - An Introduction . Springer, Berlin 2005, ISBN 3-540-23777-1 , pp. 132-135 .
  9. ↑ I. Gawdiak, H. Fedor (ed.): NASA Historical Data book . Vol. IV: NASA Resources 1969-1978. Nasa History Office, Washington 1994, p. 401 .
personal data
SURNAME Fehlberg, Erwin
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH September 8, 1911
PLACE OF BIRTH Berlin
DATE OF DEATH November 1990
Place of death Huntsville, Alabama