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Substitution methods for the automatic symbolic solution of differential equations of first order and first degree

  • 5. Differential Equations
  • Conference paper
  • First Online:
Book cover Symbolic and Algebraic Computation (EUROSAM 1979)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 72))

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Abstract

Some heuristics that suggest substitutions for solving differential equations of first order and first degree are presented. The test results with these heuristics show that ‘satisfying’ heuristics can be developed for this type of differential equations. Moreover, test results show that a program utilizing the basic elementary solution methods and a comparatively small set of such heuristics is able to solve most of the elementarily solvable differential equations of first order and first degree, which are collected in the textbooks of Kamke and Murphy.

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References

  • Kamke, E. (1961): "Differentialgleichungen — Lösungsmethoden und Lösungen, 1. Gewöhnliche Differentialgleichungen", Akad. Verl. Ges. Geest&Portig K.G., Leipzig, 7th edition.

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  • Moses, J. (1967): "Symbolic Integration", Report MAC TR-47, Project MAC, MIT, Cambr., Mass., Dec 1967.

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  • Murphy, G.M. (1960): "Ordinary Differential Equations", D. van Nostrand Comp., Inc., Princeton, New Jersey.

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  • ODER (1976): Listing of the program ODER, MIT, Aug. 1976.

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  • Schmidt, P. (1976): "Automatic Symbolic Solution of Differential Equations of First Order and First Degree", 1976 ACM Symposium on Symbolic and Algebraic Computation, Yorktown Heights, N.Y., Aug. 1976, pp. 114–125.

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  • Schmidt, P. (1977): "Maschinelle symbolische Lösung von Differentialgleichungen 1. Ordnung und 1. Grades", Informatik Berichte der Universität Bonn, Nr. 17, Nov. 1977.

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Authors and Affiliations

  1. Institut für Informatik, Universität Bonn, Wegelerstr. 6, 5300, Bonn, West Germany

    Peter Schmidt

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  1. Peter Schmidt
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Edward W. Ng

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© 1979 Springer-Verlag Berlin Heidelberg

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Schmidt, P. (1979). Substitution methods for the automatic symbolic solution of differential equations of first order and first degree. In: Ng, E.W. (eds) Symbolic and Algebraic Computation. EUROSAM 1979. Lecture Notes in Computer Science, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09519-5_69

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  • DOI: https://doi.org/10.1007/3-540-09519-5_69

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09519-4

  • Online ISBN: 978-3-540-35128-3

  • eBook Packages: Springer Book Archive

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