Computer model of point sources in control problems for heating bodies

Abstract

In this article we suggest a computer model for heat sources used in control problems of heating bodies. It is assumed that the sources have point support, which forces to involve generalized functions, more specifically Dirac's function and its derivatives. In theory Dirac's function and its derivatives have rigor symbolic definition, but in practice it is impossible to implement them using those symbolic notions. Using Lloc approximations to Dirac's function, a way how it can be implemented is suggested. Main attention is paid to problems modeling control of heating of bodies with point sources. Corresponding numerical examples are provided and discussed.