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1994 | 29 | 1 | 215-225
Tytuł artykułu

About stability estimates and resolvent conditions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
29
Numer
1
Strony
215-225
Opis fizyczny
Daty
wydano
1994
Twórcy
  • Department of Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
  • Department of Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
  • Department of Mathematics and Computer Science, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
Bibliografia
  • [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York 1965.
  • [2] F. F. Bonsall and J. Duncan, Numerical ranges, in: Studies in Functional Analysis, R. G. Bartle (ed.), Mathematical Association of America, 1980, 1-49.
  • [3] Ph. Brenner and V. Thomée, On rational approximations of semigroups, SIAM J. Numer. Anal. 16 (1979), 683-694.
  • [4] J. B. Conway, A Course in Functional Analysis, Springer, New York 1985.
  • [5] M. Crouzeix, On multistep approximation of semigroups in Banach spaces, J. Comput. Appl. Math. 20 (1987), 25-35.
  • [6] D. F. Griffiths, I. Christie and A. R. Mitchell, Analysis of error growth for explicit difference schemes in conduction-convection problems, Internat. J. Numer. Methods Engrg. 15 (1980), 1075-1081.
  • [7] R. D. Grigorieff, Time discretization of semigroups by the variable two-step BDF method, in: Numerical Treatment of Differential Equations, K. Strehmel (ed.), Teubner, Leipzig 1991, 204-216.
  • [8] P. Henrici, Applied and Computational Complex Analysis, vol. 2, Wiley, New York 1977.
  • [9] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge Univ. Press, 1990.
  • [10] J. F. B. M. Kraaijevanger, H. W. J. Lenferink and M. N. Spijker, Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations, J. Comput. Appl. Math. 20 (1987), 67-81.
  • [11] H. O. Kreiss, Über die Stabilitätsdefinition für Differenzengleichungen die partielle Differentialgleichungen approximieren, BIT 2 (1962), 153-181.
  • [12] H. O. Kreiss, Well posed hyperbolic initial boundary value problems and stable difference approximations, in: Proc. Third Internat. Conf. on Hyperbolic Problems, Uppsala, Sweden, 1990.
  • [13] H. O. Kreiss and L. Wu, On the stability definition of difference approximations for the initial boundary value problem, Appl. Numer. Math. 12 (1993), 213-227.
  • [14] G. I. Laptev, Conditions for the uniform well-posedness of the Cauchy problem for systems of equations, Soviet Math. Dokl. 16 (1975), 65-69.
  • [15] H. W. J. Lenferink and M. N. Spijker, The relevance of stability regions in the numerical solution of initial value problems, in: Numerical Treatment of Differential Equations, K. Strehmel (ed.), Teubner, Leipzig 1988, 95-103.
  • [16] H. W. J. Lenferink and M. N. Spijker, A generalization of the numerical range of a matrix, Linear Algebra Appl. 140 (1990), 251-266.
  • [17] H. W. J. Lenferink and M. N. Spijker, On the use of stability regions in the numerical analysis of initial value problems, Math. Comp. 57 (1991), 221-237.
  • [18] H. W. J. Lenferink and M. N. Spijker, On a generalization of the resolvent condition in the Kreiss matrix theorem, ibid., 211-220.
  • [19] R. J. LeVeque and L. N. Trefethen, On the resolvent condition in the Kreiss matrix theorem, BIT 24 (1984), 584-591.
  • [20] Ch. Lubich, On the convergence of multistep methods for nonlinear stiff differential equations, Numer. Math. 58 (1991), 839-853.
  • [21] Ch. Lubich and O. Nevanlinna, On resolvent conditions and stability estimates, BIT 31 (1991), 293-313.
  • [22] C. A. McCarthy and J. Schwartz, On the norm of a finite boolean algebra of projections, and applications to theorems of Kreiss and Morton, Comm. Pure Appl. Math. 18 (1965), 191-201.
  • [23] J. Miller, On the resolvent of a linear operator associated with a well-posed Cauchy problem, Math. Comp. 22 (1968), 541-548.
  • [24] J. Miller and G. Strang, Matrix theorems for partial differential and difference equations, Math. Scand. 18 (1966), 113-123.
  • [25] K. W. Morton, On a matrix theorem due to H. O. Kreiss, Comm. Pure Appl. Math. 17 (1964), 375-379.
  • [26] O. Nevanlinna, Remarks on time discretization of contraction semigroups, Helsinki Univ. Techn., Inst. Math., report HTKK-MAT-A225 (1984).
  • [27] S. V. Parter, Stability, convergence, and pseudo-stability of finite-difference equations for an over-determined problem, Numer. Math. 4 (1962), 277-292.
  • [28] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York 1983.
  • [29] C. Pearcy, An elementary proof of the power inequality for the numerical radius, Michigan Math. J. 13 (1966), 289-291.
  • [30] S. C. Reddy and L. N. Trefethen, Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues, Comput. Methods Appl. Mech. Engrg. 80 (1990), 147-164.
  • [31] S. C. Reddy and L. N. Trefethen, Stability of the method of lines, Numer. Math. 62 (1992), 235-267.
  • [32] R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed., Wiley, New York 1967.
  • [33] M.-N. Le Roux, Semidiscretization in time for parabolic problems, Math. Comp. 33 (1979), 919-931.
  • [34] W. Rudin, Functional Analysis, McGraw-Hill, New York 1973.
  • [35] J. C. Smith, An inequality for rational functions, Amer. Math. Monthly 92 (1985), 740-741.
  • [36] M. N. Spijker, Stepsize restrictions for stability of one-step methods in the numerical solution of initial value problems, Math. Comp. 45 (1985), 377-392.
  • [37] M. N. Spijker, On a conjecture by LeVeque and Trefethen related to the Kreiss matrix theorem, BIT 31 (1991), 551-555.
  • [38] E. Tadmor, The equivalence of $L_2$-stability, the resolvent condition and strict H-stability, Linear Algebra Appl. 41 (1981), 151-159.
  • [39] L. N. Trefethen, Non-normal matrices and pseudospectra, in preparation.
  • [40] E. Wegert and L. N. Trefethen, From the Buffon needle problem to the Kreiss matrix theorem, Amer. Math. Monthly, to appear.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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