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On the numerical solution of the equations of propagation by the method of characteristics

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Summary

A new application of the method of characteristics for the numerical solution of the problems of one-dimensional propagation is stated. The main concept is to consider a Massau grid and to compel it into a net of rectangles, having the sides parallel to the axes of the space-time plane.

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References

  1. See, for other details, the treatise: F. Tricomi,Equazioni a derivate parziali, Cremonese, Roma 1957, the symbolism of which is also generally followed.

  2. See, for the relevant demonstrations: R. Courant and K.O. Friedrichs,Supersonic Flow and Shock Waves, Interscience Publishers New York, 1948.

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  3. B. Riemann,Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite, Abh. Goettingen, 1860.

  4. J. Massau,Mémoire sur l'integration graphique des equations aux derivées partielles, Mem. Ass. Ing. Gand, 1900.

  5. See on this subject the article of M. Lister,The numerical solution of hyperbolic partial differential equations by the method of characteristics, in the treatise: A. Ralston, H. S. Wilf,Mathematical methods for digital computers, Wiley, New York, 1960 and the text:Numerical solution of ordinary and partial differential equations, published by L. Fox, Pergamon Press, New York, 1962.

  6. The general method of interpolation by successive differences is amply developed in: F. B. Hildebrand, Introduction to numerical analysis, Mc Graw-Hill, New York, 1956.

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  7. In a particular case, that of the linear equations with constant coefficients, the stated condition is also sufficient. The relevant demonstration is in the work: R. Courant, K.O. Friedrichs, H. Lewy,Ueber die partiellen Differenzengleichungen der Mathematischen Physik, Mathematische Annalen, 1928.

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Authors and Affiliations

  1. Università di Bologna, Italy

    Giuseppe Evangelisti (Professore di Costruzioni Idrauliche)

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  1. Giuseppe Evangelisti
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Evangelisti, G. On the numerical solution of the equations of propagation by the method of characteristics. Meccanica 1, 29–36 (1966). https://doi.org/10.1007/BF02128405

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  • DOI: https://doi.org/10.1007/BF02128405

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