On numerical integration of ordinary differential equations
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- by Arnold Nordsieck PDF
- Math. Comp. 16 (1962), 22-49 Request permission
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
- William Edmund Milne, Numerical solution of differential equations, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1953. MR 0068321
- Lothar Collatz, Numerische Behandlung von Differentialgleichungen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band 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 10.1007/bf02080985 E. Fehlberg, “Numerically stable interpolation formulas with favorable error propagation for first and second order differential equations,” NASA Technical Note D-599, March 1961.
Additional Information
- © Copyright 1962 American Mathematical Society
- Journal: Math. Comp. 16 (1962), 22-49
- MSC: Primary 65.61
- DOI: https://doi.org/10.1090/S0025-5718-1962-0136519-5
- MathSciNet review: 0136519