Informatica

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.

The convergence properties of some LOD schemes are considered. New stability estimates with respect to boundary conditions are proved. These results are used to investigate the accuracy of LOD schemes when no special boundary correction technique is used for the realization of LOD schemes. The accuracy of LOD schemes with corrected boundary conditions is also investigated. Results of the computational experiment are given.