Abstract
In the paper, the stability conditions of a three-layer symmetric differential-difference scheme with a weight parameter in the class of functions summable on a network-like domain are obtained. To analyze the stability of the differential-difference system in the space of feasible solutions H, a composite norm is introduced that has the structure of a norm in the space H^2=H⊕H. Namely, for Y={Y_1,Y_2}∈H^2, Y_l∈H (l=1,2), 〖∥Y∥〗_H^2 = 〖∥Y_1∥〗_(1,H)^2+〖∥Y_2∥〗_(2,H)^2, where 〖∥•∥〗_(1,H)^2 〖∥•∥〗_(2,H)^2 are some norms in H. The use of such a norm in the description of the energy identity opens the way for constructing a priori estimates for weak solutions of the differential-difference system, convenient for practical testing in the case of specific differentialdifference schemes. The results obtained can be used to analyze optimization problems that arise when modeling network-like transfer processes with the help of formalisms of differentialdifference systems.
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