Affiliations: Vilnius University Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania, e-mail: mifodijus.sapagovas@mii.vu.lt | Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania, e-mail: regimantas.ciupaila@vgtu.lt | Lithuanian University of Health Sciences, Vytautas Magnus University, Eivenių 4, LT-50009 Kaunas, Lithuania, e-mail: zivile.je@gmail.com | Vilnius University, Faculty of Mathematics and Informatics, Naugarduko 24, LT-03225 Vilnius, Lithuania, e-mail: tadas.meskauskas@mif.vu.lt
Note: [] Corresponding author.
Abstract: 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.
