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Numerical Method for Solving Discontinuous Initial/Final-Value Problems

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Abstract

Ordinary differential systems with initial/final value problems are a subclass of two point boundary value problems, which arise in many applications, in physics, materials science, optimal control, economics, business administration and others.

The standard method for solving these problems are sensitive to a lack of continuity in the equations. In this manuscript, a novel method for solving this problem is presented. This method is based on embedding of the original ODE system in a hyperbolic PDE system.

The efficacy of this method is demonstrated using a numerical example.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Adi Ditkowski

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  1. Adi Ditkowski
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Correspondence to Adi Ditkowski.

Additional information

This research was supported by the ISRAEL SCIENCE FOUNDATION (grant No. 1364/04) and the UNITED STATES-ISRAEL BINATIONAL SCIENCE FOUNDATION (grant No. 2004099).

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Ditkowski, A. Numerical Method for Solving Discontinuous Initial/Final-Value Problems. J Sci Comput 37, 268–281 (2008). https://doi.org/10.1007/s10915-008-9243-3

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  • DOI: https://doi.org/10.1007/s10915-008-9243-3

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