On those ordinary differential equations that are solved exactly by the improved Euler method

Hans Jakob Rivertz

Archivum Mathematicum (2013)

  • Volume: 049, Issue: 1, page 29-34
  • ISSN: 0044-8753

Abstract

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As a numerical method for solving ordinary differential equations y ' = f ( x , y ) , the improved Euler method is not assumed to give exact solutions. In this paper we classify all cases where this method gives the exact solution for all initial conditions. We reduce an infinite system of partial differential equations for f ( x , y ) to a finite system that is sufficient and necessary for the improved Euler method to give the exact solution. The improved Euler method is the simplest explicit second order Runge-Kutta method.

How to cite

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Rivertz, Hans Jakob. "On those ordinary differential equations that are solved exactly by the improved Euler method." Archivum Mathematicum 049.1 (2013): 29-34. <http://eudml.org/doc/252516>.

@article{Rivertz2013,
abstract = {As a numerical method for solving ordinary differential equations $y^\{\prime \}=f(x,y)$, the improved Euler method is not assumed to give exact solutions. In this paper we classify all cases where this method gives the exact solution for all initial conditions. We reduce an infinite system of partial differential equations for $f(x,y)$ to a finite system that is sufficient and necessary for the improved Euler method to give the exact solution. The improved Euler method is the simplest explicit second order Runge-Kutta method.},
author = {Rivertz, Hans Jakob},
journal = {Archivum Mathematicum},
keywords = {extended Euler; numerics; ordinary differential equations; extended Euler; numerics; ordinary differential equations},
language = {eng},
number = {1},
pages = {29-34},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On those ordinary differential equations that are solved exactly by the improved Euler method},
url = {http://eudml.org/doc/252516},
volume = {049},
year = {2013},
}

TY - JOUR
AU - Rivertz, Hans Jakob
TI - On those ordinary differential equations that are solved exactly by the improved Euler method
JO - Archivum Mathematicum
PY - 2013
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 049
IS - 1
SP - 29
EP - 34
AB - As a numerical method for solving ordinary differential equations $y^{\prime }=f(x,y)$, the improved Euler method is not assumed to give exact solutions. In this paper we classify all cases where this method gives the exact solution for all initial conditions. We reduce an infinite system of partial differential equations for $f(x,y)$ to a finite system that is sufficient and necessary for the improved Euler method to give the exact solution. The improved Euler method is the simplest explicit second order Runge-Kutta method.
LA - eng
KW - extended Euler; numerics; ordinary differential equations; extended Euler; numerics; ordinary differential equations
UR - http://eudml.org/doc/252516
ER -

References

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