Enclosures and semi-analytic discretization of boundary value problems

Grossmann, c.

Banach Center Publications, Tome 29 (1994), p. 283-304 / Harvested from The Polish Digital Mathematics Library

Détail

Publié le : 1994-01-01

Zbl 0802.65072

EUDML-ID : urn:eudml:doc:262668

Bibliographie

[000] [1] H. Abhari and C. Grossmann, Approximate bases for boundary value problems and applications to MID-techniques, Z. Angew. Math. Mech. 72 (1992), 83-91. | Zbl 0763.65062

[001] [2] H. Abhari and M. Al-Zanaidi, Computational aspects of monotone iteration discretization algorithm, preprint, TU Dresden, 07-01-88.

[002] [3] R. A. Adams, Sobolev Spaces, Academic Press, New York 1975.

[003] [4] E. Adams, Invers-Monotonie, direkte und indirekte Intervallmethoden, Forschungszentrum Graz, Ber. 185 (1982). | Zbl 0506.65021

[004] [5] E. Adams, R. Ansorge, C. Grossmann and H.-G. Roos (eds.), Discretization in Differential Equations and Enclosures, Akademie-Verlag, Berlin 1987. | Zbl 0636.00010

[005] [6] E. Adams, D. Cordes and H. Keppler, Enclosure methods as applied to linear periodic ODEs and matrices, Z. Angew. Math. Mech. 70 (1990), 565-578. | Zbl 0739.65059

[006] [7] E. Adams und H. Spreuer, Konvergente numerische Schrankenkonstruktionen mit Spline-Funktionen für nichtlineare gewöhnliche bzw. parabolische Randwertaufgaben, in: K. Nickel (ed.), Interval Mathematics, Springer, Berlin 1975. | Zbl 0304.65072

[007] [8] M. Al-Zanaidi and C. Grossmann, Monotone discretization in boundary value problems using PASCAL-SC, in: I. Marek (ed.), Proc. ISNA 87, Teubner, Leipzig 1988, 91-96. | Zbl 0681.65055

[008] [9] M. Al-Zanaidi and C. Grossmann, Monotone iteration discretization algorithm for BVP's, Computing 31 (1989), 59-74.

[009] [10] M. Al-Zanaidi and C. Grossmann, 1D-grid generation by monotone iteration discretization, ibid. 34 (1990), 377-390. | Zbl 0693.65053

[010] [11] N. Anderson and A. M. Arthurs, Variational solutions of the Thomas-Fermi equations, Quart. Appl. Math. 39 (1981), 127-129. | Zbl 0462.49042

[011] [12] S. Carl, The monotone iterative technique for a parabolic boundary value problem with discontinuous nonlinearity, Nonlinear Anal. 13 (1989), 1399-1407. | Zbl 0696.35083

[012] [13] S. Carl and C. Grossmann, Iterative spline bounds for systems of boundary value problems, in: J. W. Schmidt and H. Späth (eds.), Splines in Numerical Analysis, Akademie-Verlag, Berlin 1989, 19-30. | Zbl 0673.65042

[013] [14] S. Carl and C. Grossmann, Monotone enclosure for elliptic and parabolic systems with nonmonotone nonlinearities, J. Math. Anal. Appl. 151 (1990), 190-202. | Zbl 0778.65074

[014] [15] S. Carl and S. Heikkilä, On extremal solutions of an elliptic boundary value problem involving discontinuous nonlinearities, preprint, Univ. Oulu, 1990; to appear in Differential Integral Equations. | Zbl 0785.35034

[015] [16] C. Y. Chan and Y. C. Hon, A constructive solution for a generalized Thomas-Fermi theory of ionized atoms, Quart. Appl. Math. 45 (1987), 591-599. | Zbl 0639.34021

[016] [17] R. C. Duggan and C. Goodmann, Pointwise bounds for a nonlinear heat conduction model of the human head, Bull. Math. Biol. 48 (1986), 229-236. | Zbl 0585.92011

[017] [18] A. Felgenhauer, Monotone discretization of the Poisson equation in the plane, to appear.

[018] [19] R. C. Flagg, C. D. Luning and W. L. Perry, Implementation of new iterative techniques for solutions of Thomas-Fermi and Emden-Fowler equations, J. Comput. Phys. 38 (1980), 396-405. | Zbl 0456.65054

[019] [20] E. C. Gartland, On the uniform convergence of the Scharfetter-Gummel discretization, preprint, Kent State Univ., Feb. 1991. | Zbl 0765.65112

[020] [21] E. C. Gartland and C. Grossmann, Semianalytic solution of boundary value problems by using approximated operators, Z. Angew. Math. Mech. 72 (1992), 615-619. | Zbl 0771.65045

[021] [22] C. Grossmann, Monotone Einschließung höherer Ordnung für 2-Punkt-Randwertauf- gaben, Z. Angew. Math. Mech. 67 (1987), T475-T477.

[022] [23] C. Grossmann, Monotone discretization of two-point boundary value problems and related numerical methods, in [5], 99-122.

[023] [24] C. Grossmann, Semianalytic discretization of weakly nonlinear boundary value problems with variable coefficients. Z. Anal. Anwendungen 10 (1991), 513-523. | Zbl 0760.65077

[024] [25] C. Grossmann, Enclosures of the solution of the Thomas-Fermi equation by monotone discretization, J. Comput. Phys. (1992), 26-38.

[025] [26] C. Grossmann und M. Krätzschmar, Monotone Diskretisierung und adaptive Gittergenerierung für Zwei-Punkt-Randwertaufgaben, Z. Angew. Math. Mech. 65 (1985), T264-T266. | Zbl 0621.65093

[026] [27] C. Grossmann, M. Krätzschmar und H.-G. Roos, Gleichmäßig einschließende Diskretisierungsverfahren für schwach nichtlineare Randwertaufgaben, Numer. Math. 49 (1986), 95-110. | Zbl 0621.65092

[027] [28] C. Grossmann and H.-G. Roos, Feedback grid generation via monotone discretization for two-point boundary-value problems, IMA J. Numer. Anal. 6 (1986), 421-432. | Zbl 0655.65105

[028] [29] C. Grossmann and H.-G. Roos, Uniform enclosure of high order for boundary value problems by monotone discretization, Math. Comp. 53 (1989), 609-617. | Zbl 0673.34025

[029] [30] C. Grossmann and H.-G. Roos, Convergence analysis of higher order monotone discretization, Wiss. Z. Tech. Univ. Dresden 38 (1989), 155-168. | Zbl 0675.65081

[030] [31] C. Grossmann and H.-G. Roos, Enclosing discretization for singular and singularly perturbed boundary value problems, in: H.-G. Roos, A. Felgenhauer and L. Angermann (eds.), Numerical Methods in Singular Perturbed Problems, TU Dresden, 1991, 71-82.

[031] [32] G. Koeppe, H.-G. Roos and L. Tobiska, An enclosure generating modification of the method of discretization in time, Comment. Math. Univ. Carolin. 28 (1987), 447-453. | Zbl 0635.65122

[032] [33] M. Krätzschmar, Iterationsverfahren zur Lösung schwach nichtlinearer elliptischer Randwertaufgaben mit monotoner Lösungseinschließung, Dissertation, TU Dresden, 1983.

[033] [34] U. Kulisch (ed.), PASCAL-SC, Pascal Extension for Scientific Computation, Wiley, New York and Teubner, Stuttgart 1987.

[034] [35] G. S. Ladde, V. Lakshmikantham and A. S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, 1985. | Zbl 0658.35003

[035] [36] R. Lohner, Einschließung der Lösung gewöhnlicher Anfangs- und Randwertaufgaben und Anwendungen, Dissertation, Univ. Karlsruhe, 1988. | Zbl 0663.65074

[036] [37] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York 1970. | Zbl 0241.65046

[037] [38] M. Plum, Numerical existence proofs and explicit bounds for solutions of nonlinear elliptic boundary value problems, to appear.

[038] [39] H.-G. Roos, The Rothe method and monotone discretization for parabolic equations, in [5], 155-166.

[039] [40] H.-G. Roos, Uniformly enclosing discretization methods and grid generation for semilinear boundary value problems with first order terms, Apl. Mat. 34 (1989), 274-284. | Zbl 0685.65069

[040] [41] H.-G. Roos, A uniformly convergent discretization method for singularly perturbed boundary value problems of the fourth order, Zb. Rad. Prirod.-Mat. Fak. Novi Sad Ser. Mat. 19 (1989), 51-64. | Zbl 0719.65067

[041] [42] H.-G. Roos, Global uniformly convergent schemes for a singularly perturbed boundary-value problem using patched base spline functions, J. Comput. Appl. Math. 29 (1990), 69-77. | Zbl 0686.65048

[042] [43] H.-G. Roos, Uniform enclosing discretization methods for semilinear boundary value problems, in: Nonlinear Analysis and Mathematical Modelling, Banach Center Publ. 24, PWN, Warszawa 1990, 257-268.

[043] [44] J. W. Schmidt, Ein Einschließungsverfahren für Lösungen fehlerbehafteter linearer Gleichungen, Period. Math. Hungar. 13 (1982), 29-37. | Zbl 0496.65014

[044] [45] J. Schröder, Operator Inequalities, Academic Press, New York 1980.

[045] [46] J. Schröder, A method for producing verified results for two-point boundary value problems, in: Comput. Suppl. 6, Springer, Vienna 1988, 9-22.

[046] [47] J. Schröder, Operator inequalities and applications, in: E. W. Norrie (ed.), Inequalities, Marcel Dekker, New York 1991, 163-210.

[047] [48] J. Sprekels and H. Voss, Pointwise inclusions of fixed points by finite dimensional iteration schemes, Numer. Math. 32 (1979), 381-392. | Zbl 0393.65052

[048] [49] G. Vanden Berghe and H. De Meyer, Accurate computation of higher Sturm-Liouville eigenvalues, to appear. | Zbl 0716.65079

[049] [50] R. Voller, Enclosure of solutions of weakly nonlinear elliptic boundary value problems and their computation, Computing 42 (1989), 245-258. | Zbl 0681.65076

[050] [51] W. Walter, Differential and Integral Inequalities, Springer, Berlin 1970.

[051] [52] J. Weissinger, A kind of difference methods for enclosing solutions of ordinary linear boundary value problems, in: Comput. Suppl. 6, Springer, Vienna 1988, 23-32. | Zbl 0658.65072