Abstract
Modifying a two-stage algorithm given by PETRYSHYN [11] and BREZISSIBONY
Teil einer modifizierten Fassung der Dissertation des Autors an der Universität München.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literatur
AMES, W.: Nonlinear partial differential equations in engineering. Academic Press, New York (1965).
BELLMAN, R., KALABA, R.: Quasilinearization and nonlinear boundary value problems. Elsevier, New York (1965).
BREZIS, H., SIBONY, M.: Méthodes d'approximation de d'itération pour les opérateurs monotones. Arch.Rat.Mech.Anal. 28, 59–82 (1968).
BROWDER, F.: The solvability of non-linear functional equations. Duke Math.J. 30, 557–566 (1963).
COLLATZ, L.: Funktionalanalysis und numerische Mathematik. Springer, Berlin,Heidelberg,New York (1968).
D'YAKONOV, E.G.: On the solution of some elliptic difference equations. J.Inst.Maths Applics 7, 1–20 (1971).
FREHSE, J.: Existenz und Konvergenz von Lösungen nichtlinearer elliptischer Differenzengleichungen unter DIRICHLET-Randbedingungen. Math.Z. 109, 311–343 (1969).
KOSELEV, A.: Convergence of the method of successive approximation for quasilinear elliptic equations. Soviet Math.Dokl. 3, 219–222 (1962).
LADYSHENSKAYA, O., URAL'TSEVA, N.: Linear and quasilinear elliptic equations. Academic Press, New York (1968)
LEES, M.: Alternating direction and semi-explicit difference methods for parabolic differential equations. Num.Math. 3, 398–412 (1961).
PETRYSHYN, W.: On the extension and the solution of non linear operator equations. Ill.J.Math. 10, 255–274 (1966).
SAPAGOVAS, M.: The method of finite differences for the solution of quasilinear elliptic equations with discontinuous coefficients. USSR Comp.Math. and Math.Phys. 5, 72–85 (1965).
SERRIN, J.: The problem of DIRICHLET for quasilinear elliptic differential equations with many independent variables. Phil.Trans.Roy.Soc.London, Series A. 264, 413–496 (1969)
SIBONY, M.: Méthodes itératives pour les équations et inéquations aux dérivées partielles non linéaires de type monotone. Calcolo 7, 65–183 (1970).
Editor information
Rights and permissions
Copyright information
© 1972 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Sachs, A. (1972). Iterationsverfahren für elliptische (nichtlineare) Differenzenoperatoren in Divergenzform. In: Ansorge, R., Törnig, W. (eds) Numerische Lösung nichtlinearer partieller Differential- und Integrodifferentialgleichungen. Lecture Notes in Mathematics, vol 267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061624
Download citation
DOI: https://doi.org/10.1007/BFb0061624
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-05895-3
Online ISBN: 978-3-540-37540-1
eBook Packages: Springer Book Archive