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Stability of iterative schemes for nonselfadjoint equations. (English) Zbl 0343.65037

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65J05 General theory of numerical analysis in abstract spaces
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References:

[1] J. E. Gunn: The Solution of elliptic difference equations by semiexplicit iterative techniques. SIAM J. Numer. Anal. 2, 24-45 (1964). · Zbl 0137.33301
[2] M. M. Gupta: Convergence and stability of finite difference schemes for some elliptic equations. Ph. D. thesis, University of Saskatchewan, Saskatoon, Canada (1971).
[3] L. V. Kantorovich G. P. Akilov: Functional analysis in normed spaces. New York: Pergamon Press 1964. · Zbl 0127.06104
[4] H. O. Kreiss: Über die Stabilitätsdefinition für Differenzengleichungen die partieile Differentialgleichungen approximieren. Nordisk Tidskr. Informations - Behandling (BIT) 2, 153-181 (1962). · Zbl 0109.34702
[5] P. D. Lax, and B. Wendroff: Difference schemes for hyperbolic equations with high order of accuracy. Comm. Pure Appl. Math. 17, 381-398 (1964). · Zbl 0233.65050
[6] G. G. O’Brian M. A. Hyman, and S. Kaplan: A study of the numerical solution of partial differential equations. J. Math, and Phys. 29, 223 - 251 (1951). · Zbl 0042.13204
[7] R. D. Richtmyer, K. W. Morton: Difference methods for initialvalue problems. 2nd, New York: Interscience 1967. · Zbl 0155.47502
[8] V. S. Ryabenkii, and A. F. Filippov: Über die Stabilität von Differenzengleichungen. Berlin; Deutscher Verlag der Wissenschaften 1960.
[9] A. A. Samarskii: Classes of Stable Schemes. Ž. Vyčisl. Mat. i Mat. Fiz. 7, 1096-1133 (1967).
[10] A. A. Samarskii: Necessary and Sufficient conditions for the stability of two-layer difference schemes. Soviet Math. Dokl. 9, 946-950 (1968). · Zbl 0179.20201
[11] A. A. Samarskii: Two layer iteration schemes for nonselfadjoint equations. Soviet Math. Dokl. 10, 554-558 (1969). · Zbl 0189.44002
[12] V. Thomée: Stability theory for partial difference operators. SIAM Rev. 11, 152-195 (1969). · Zbl 0176.09101
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