Computational experiment for stability analysis of difference schemes with nonlocal conditions

Abstract

Straipsnyje aprašyta metodika, kaip gauti naujus diferencialinių lygčių skaitinių algoritmų rezultatus, naudojant skaičiavimo eksperimentą kaip tyrimo metodą. Pateikti nauji rezultatai apie parabolinių lygčių su nelokaliosiomis integralinėmis sąlygomis skirtuminių schemų stabilumą

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 \alpha(x) and \beta(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