Journal of Theoretical
and Applied Mechanics

18, 1, pp. 71-86, Warsaw 1980

Zastosowanie transformacji Laplace'a w metodzie uśredniania poprawek funkcjonalnych

Zbigniew Nowak, Kazimierz Rup

This paper constitutes an extension of the averaging method of functional corrections discussed and applied in [2] to a differential parabolic equation of transport phenomena. The method in consideration is here used in the region of Laplace transform. The procedure makes it possible to determine the initial values without using additional conditions. Morever it is shown that such an application of the method discussed determines in a natural way the condition from which the initial values are to be found when the Laplace transform is not being employed. In the case discussed it is the condition of the minimum of integral deviation. It was pointed put in a numerical example that a very good accuracy of the trial solution already in the second approximation step was obtained. Besides, different trial solutions of the equation discussed in the paper [2] were compared when choosing two conditions for determinating the initial values i.e. the condition of the minimum of integral deviation and that of the minimum of integral quadratic deviation. It was pointed out that the second condition gives a better accuracy of the trial solution with respect to the exact one.