Artificial intelligence

Abstract: The class of mathematical models of processes in the linear systems with the fixed states is offered in the paper. Such mathematical models are the discrete analogues of Volterra integral equations of the second kind. The methods of analytical solutions of the offered equations on the basis of finding of solutions of corresponding equations binding the kernel and resolvent are considered. The theorem, defining the analytical kind of resolvent on the given kernel for some important special cases, namely at the separable type of kernel, is considered and proved. Equivalent transformations of the offered mathematical models to the linear difference equations are considered.

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