Volume 24, Issue 2 (2013), pp. 275–290
Based on an example, we describe how outcomes of computational experiment can be employed for study of stability of numerical algorithm, provided that related theoretical propositions are not proven yet. More precisely, we propose a systematic and generalized methodology, how to investigate the influence of the weight functions α(x) and β(x), present in the integral boundary conditions, on the stability of difference schemes, for some class of parabolic equations. The ground of the methodology is the investigation of the spectrum of a matrix, defining the transition to the upper layer of the difference scheme. Spectral structure of this matrix is analysed by both analytic method and computational experiment.
Volume 3, Issue 2 (1992), pp. 159–172
This paper is devoted to the investigation of difference schemes for the solution of an important free-surface problem: modelling of a liquid-metal contact. The existence of a solution and the convergence of proposed iterative processes are investigated in a weak sense, using the alternative form of the problem as a nonlinear constrained minimization problem.