ACTUAL STABILITY CRITERIA FOR A 1-D HEAT CONDUCTION EQUATION. PART I. THE MAIN SPECTPUM THEOREM FOR A ONE-REGION PROBLEM

N. A. Ismailova, V. Ye. Konclrashov
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1982. Вып.2. С. 41-48.

      This paper represents the first portion of efforts aimed at examining the impact of boundary conditions, set as a linear flux/temperature combination, on a two-layer difference scheme stability which approximates a 1-D linear heat conduction equation. Heat conductivity, space step, and upper layer weight are assumed to be variable quantities. Several spectral system representations are given, spectral system running ratios are estimated, and all transition matrix eigenvalues are proved to be always real.