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 importa nt concern in computational heat transfer applications. As such, the presen t paper describes a formal basis towards providing the theoretical concepts , evolution and development and characterization of a wide class of time di scretized operators for transient heat transfer computations. Therein, eman ating from a common family tree and explained via a generalized time weight ed philosophy, the paper addresses the development and et)evolution of time integral operators [IO], and leading to integration operators [InO] in tim e encompassing single-step integration operators [SSInO], multi-step integr ation operators [MSInO], and a class of finite element in time integration operators [FETInO] including the relationships and the resulting consequenc es. Also depicted are those termed as discrete numerically assigned [DNA] a lgorithmic markers essentially comprising of both: the weighted time fields , and the corresponding conditions imposed upon the dependent variable appr oximation, to uniquely characterize a wide class of transient algorithms. T hereby, providing a plausible standardized formal ideology when referring t o and/or relating time discretized operators applicable to transient heat t ransfer computations.