We consider difference schemes for the heat equation with nonlocal boundary conditions containing a parameter γ > 1. Neither the original problem nor its approximating difference scheme is stable in the initial values. An algorithm is proposed to construct the stability boundaries in subspaces generated by stable harmonics. Examples of stability boundaries are given for two-layer schemes with various weights.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. A. Samarskii, Theory of Finite-Difference Schemes [in Russian], 3rd Ed., Nauka, Moscow (1989).
A. B. Gulin, N. I. Ionkin, and V. A. Morozova, Difference Schemes for Nonstationary Nonlocal Problems [in Russian], Izd. MGU, Moscow (2010).
A. B. Gulin, “Spectral stability in subspaces of difference schemes with nonlocal boundary conditions,” Diff. Uravn., 49, No. 7, 844–852 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 43, 2013, pp. 5–14.
Rights and permissions
About this article
Cite this article
Gulin, A.V. Stability Boundaries of Difference Schemes in Subspaces. Comput Math Model 25, 297–305 (2014). https://doi.org/10.1007/s10598-014-9226-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-014-9226-1