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Numerische Mathematik

, Volume 31, Issue 2, pp 131–152 | Cite as

One-step methods of any order for ordinary differential equations with discontinuous right-hand sides

  • Reinhold Mannshardt
Article

Summary

The right-hand sides of a system of ordinary differential equations may be discontinuous on a certain surface. If a trajectory crossing this surface shall be computed by a one-step method, then a particular numerical analysis is necessary in a neighbourhood of the point of intersection. Such an analysis is presented in this paper. It shows that one can obtain any desired order of convergence if the method has an adequate order of consistency. Moreover, an asymptotic error theory is developed to justify Richardson extrapolation. A general one-step method is constructed satisfying the conditions of the preceding theory. Finally, a simplified Newton iteration scheme is used to implement this method.

Subject Classifications

AMS(MOS): 65L05 CR: 5.17 

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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Reinhold Mannshardt
    • 1
  1. 1.Rechenzentrum der Ruhr-UniversitätBochumGermany (Fed. Rep.)

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