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Mathematics of Computation

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On numerical integration of ordinary differential equations

Author: Arnold Nordsieck
Journal: Math. Comp. 16 (1962), 22-49
MSC: Primary 65.61
MathSciNet review: 0136519
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Abstract: A reliable efficient general-purpose method for automatic digital computer integration of systems of ordinary differential equations is described. The method operates with the current values of the higher derivatives of a polynomial approximating the solution. It is thoroughly stable under all circumstances, incorporates automatic starting and automatic choice and revision of elementary interval size, approximately minimizes the amount of computation for a specified accuracy of solution, and applies to any system of differential equations with derivatives continuous or piecewise continuous with finite jumps. ILLIAC library subroutine #F7, University of Illinois Digital Computer Laboratory, is a digital computer program applying this method.

References [Enhancements On Off] (What's this?)

  • William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons, Inc., New York; Chapman & Hall, Limited, London, 1953. MR 0068321
  • Lothar Collatz, Numerische Behandlung von Differentialgleichungen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Bd. LX, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (German). 2te Aufl. MR 0068908
  • Heinz Rutishauser, Über die Instabilität von Methoden zur Integration gewöhnlicher Differentialgleichungen, Z. Angew. Math. Phys. 3 (1952), 65–74 (German). MR 46146, DOI
  • E. Fehlberg, “Numerically stable interpolation formulas with favorable error propagation for first and second order differential equations,” NASA Technical Note D-599, March 1961.

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Article copyright: © Copyright 1962 American Mathematical Society