Abstract
In the study of difference schemes for time-dependent problems of mathematical physics, the general theory of stability (well-posedness) for operator-difference schemes is in common use. At the present time, the exact (matching necessary and sufficient) conditions for stability are obtained for a wide class of two- and three-level difference schemes considered in finite-dimensional Hilbert spaces.
The main results of the theory of stability for operator-difference schemes are obtained for problems with self-adjoint operators. In this work, we consider difference schemes for numerical solution of the Cauchy problem for first order evolution equation, where non-self-adjoint operator is represented as a product of two non-commuting self-adjoint operators. We construct unconditionally stable regularized schemes based on the solution of a grid problem with a single operator multiplier on the new time level.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker, New York (2001)
Samarskii, A.A., Gulin, A.V.: Stability of Difference Schemes. URSS, Moscow (2004). In Russian
Samarskii, A.A., Matus, P.P., Vabishchevich, P.N.: Difference Schemes with Operator Factors. Springer, Dordrecht (2002)
Acknowledgements
This work was supported by RFBR (project 14-01-00785)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Vabishchevich, P.N. (2015). Operator-Difference Scheme with a Factorized Operator. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2015. Lecture Notes in Computer Science(), vol 9374. Springer, Cham. https://doi.org/10.1007/978-3-319-26520-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-26520-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26519-3
Online ISBN: 978-3-319-26520-9
eBook Packages: Computer ScienceComputer Science (R0)