Abstract
It has been shown that the differential heat conduction equation together with the boundary conditions can be recast as a sequence consisting of integral identities for the weighted temperature. Weight functions take into account the properties of the heat conduction equation and the boundary conditions. The sequence of identities was constructed on the basis of multiple differentiation or integration operators. Using the search for eigenvalues of the boundary value problem as an example, we have demonstrated the high efficiency of such systems.
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