Conjugate-factorized models in mathematical physics problems

Linear mathematical models are studied, which are based on a certain law (laws) of conservation. It is shown that in this case the basic operators of a continuous model have initially a conjugate-factorized structure. This property allows one to simplify essentially the transfer to adequate grid models and to construct efficient algorithms to determine parameters of a model in different statements. The results obtained can be considered as further development of the theory of support operators for difference schemes of the divergent form.