A VARIATION APPROACH ТО PROBLEMS INVOLVED IN NON-LINEAR HEAT CONDUCTION IN TRANSIENT STATES

Bohdan Krajewski

Abstract


It has been proved in this paper that a partial non-linear differential equation can be reduced to the variation problem. A non-linear boundary value problem can be reduced with the application of the variation technique based on the Kantorovich method, to a set of ordinary differential equations.

The accuracy of the method in question is estimated herein by comparing solutions to problems solved with the application of the variation method, and of the other method as well.

The method for the construction of trial functions has also been presented herein. Three examples have been quoted in order to explain the above method.


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