MULTIPLE INTEGRATION OF THE HEAT-CONDUCTION EQUATION FOR A SPACE BOUNDED FROM THE INSIDE

An N-fold integration of the heat-conduction equation for a space bounded from the inside has been performed using a system of identical equalities with defi nition of the temperature function by a power polynomial with an exponential factor. It is shown that, in a number of cases, the approximate solutions obtained can be considered as exact because their errors comprise hundredths and thousandths of a percent. The method proposed for N-fold integration represents an alternative to classical integral transformations.
   
Author:  V. A. Kot
Keywords:  heat-conduction equation, multiple integration, cavity in a space, approximate integral method, approximation error, convergence
Page:  369