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.
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.