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Parallel algorithm for construction of singular surfaces in linear differential games

### S.S. Kumkov, V.S. Patsko

The paper deals with an algorithm of construction
and classification of singular surfaces in linear differential
games with fixed terminal moment and convex payoff function which
depends on two components of the phase vector. The algorithm is
embedded into the backward procedures for building level sets
of the value function.
In this backward procedure, the level set section at the next moment
is calculated using the section for the previous one.
The data obtained during these calculations are used for detection
and classification of the singular points in the new constructed section.
Unrolled through the time, these singular
points give the singular lines which go along over the
surface of the level set. Singular lines are joined in
the singular surfaces in the space of the game.
The main idea of the parallel computations is
briefly described.

## Electronic version of the article

The format in the PDF-file
kumkov_patsko_bul97eng.pdf (821 KB)
differs from the format in the book of Proceedings.

*Kumkov, S.S.; Patsko, V.S.*
**Parallel algorithm for construction of singular surfaces in linear differential games.**
Bainov, D. (ed.), Proceedings of the 8th International Colloquium on Differential Equations, Plovdiv, Bulgaria, August 18–23, 1997. Utrecht: VSP, 1998, pp. 275–284.

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