engleski

Formulation of Successive Integration Method in Heat Conduction

This paper proposes application of the successive integration method (SIM) for solving differential equation of heat conduction. The SIM is evolved from the Monte Carlo method. Although the Monte Carlo method is probabilistic in nature, the deterministic SIM can be obtained by the appropriate application of ordinary expression for the summation of elements in geometric progression. The SIM consists in successive expansion of integrated area by re-calculation of interaction coefficients between points at the actual boundary of integrated area and the arbitrary chosen set of points where the temperature will be calculated. During the process of integration, it is necessary to memorise only mentioned interaction coefficients; thus, in the most cases the required computer storage capacity will be lesser than those required even for iteration methods. That will reduce or completely eliminate the data swaps between computer core and peripheral data storage's, the result of which can be remarkable speed up of calculation process. The proposed SIM algorithm is simple, and can be easily implemented into any computer program.

successive integration method; heat conduction; Monte Carlo; differential equation

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