Towards a formal theory of development evolution and characterization of time discretized operators for heat transfer

The time-discretization process of transient equation systems is an important concern in computational heat transfer applications. As such, the present paper describes a formal basis towards providing the theoretical concepts, evolution and development, and characterization of a wide class of time discretized operators for transient heat transfer computations. Therein, emanating from a common family tree and explained via a generalized time weighted philosophy, the paper addresses the development and evolution of time integral operators [IO], and leading to integration operators [InO] in time encompassing single-step integration operators [SSInO], multi-step integration operators [MSInO], and a class of finite element in time integration operators [FETInO] including the relationships and the resulting consequences. Also depicted are those termed as discrete numerically assigned [DNA] algorithmic markers essentially comprising of both: the weighted time fields, and the corresponding conditions imposed upon the dependent variable approximation, to uniquely characterize a wide class of transient algorithms. Thereby, providing a plausible standardized formal ideology when referring to and or relating time discretized operators applicable to transient heat transfer computations.