References
- Abrashin , V. N. 1990 . On a variant of alternating direction method for solving multidimensional problems of mathematical physics . Diff. Uravn. , 26 (2) : 314 – 323 . (in Russian)
- Abrashin , V. N. 1999 . On stability of difference schemes of multicomponent alternating direction method for parabolic equations and systems . Diff. Uravn. , 35 (2) : 212 – 224 . (in Russian)
- Abrashin , V. N. , Egorov , A. A. and Zhadaeva , N. G. 2001 . On a class of additive iterative methods . Differents. Uravn. , 37 (12) : 1664 – 1673 . (in Russian)
- Abrashin , V. N. , Egorov , A. A. and Zhadaeva , N. G. 2001 . On a convergence rate of additive iterative methods . Diff. Uravn. , 37 (7) : 867 – 879 . (in Russian)
- Abrashin , V. N. and Zhadaeva , N. G. 1990 . Multicomponent alternating direction method for solving nonstationary problems of mathematical physics . Mathematical Modelling and Applied Mathematics. Moscow‐Vilnius , : 113 – 114 .
- Abrashin , V. N. and Zhadaeva , N. G. 1996 . Multicomponent alternating direction method for solving stationary problems of mathematical physics. I . Diff. Uravn. , 32 (9) : 1212 – 1221 . (in Russian)
- Abrashin , V.N. , Čiegis , R. and Pakalnyte , V. 2000 . Spectral stability analysis of one splitting iterative scheme . Proc. of the 3rd International Conference FDS2000, September 1–4, 2000, Palanga, Lithuania. Finite difference schemes: theory and applications . 2000 , Vilnius. Edited by: Čiegis , R. , Samarskii , A. and Sapagovas , M. pp. 1 – 10 . IMI .
- Bensoussan , A. , Lions , J.‐L. and Themam , R. 1975 . Decomposition, decentralization and coordination methods and their applications . Methods of Numerical Mathematics. Novosibirsk , : 144 – 274 . (in Russian)
- Čiegis , R. and Pakalnyte , V. 2001 . Spectral analysis of the convergence of multicomponent iterative methods . Differential Equations , 37 (7) : 1032 – 1035 .
- Douglas , J. and Rachford , H. 1956 . On the numerical solution of heat conduction problems in two and three space variables . Trans. Amer. Math. Soc. , 82 (2) : 421 – 439 .
- Marchuk , G. I. 1988 . Splitting‐up methods , Moscow : Nauka . (in Russian)
- Peaceman , D. and Rachford , H. 1955 . The numerical solution of parabolic and elliptic differential equations . J. Soc. Indust. Appl. Math. , 3 (1) : 28 – 42 .
- Samarskii , A. A. 1989 . Theory of difference schemes , Moscow : Nauka . (in Russian)
- Samarskii , A. A. and Vabishchevich , P. N. 1999 . Additive schemes for problems of mathematical physics , Moscow : Nauka . (in Russian)
- Yanenko , N. N. 1967 . Fractional step method for solving multidimensional problems of mathematical physics , Novosibirsk : Nauka . (in Russian)