On iterative solution of nonlinear heat-conduction and diffusion problems

Herbert Gajewski

Aplikace matematiky (1977)

  • Volume: 22, Issue: 2, page 77-91
  • ISSN: 0862-7940

Abstract

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The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.

How to cite

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Gajewski, Herbert. "On iterative solution of nonlinear heat-conduction and diffusion problems." Aplikace matematiky 22.2 (1977): 77-91. <http://eudml.org/doc/14993>.

@article{Gajewski1977,
abstract = {The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.},
author = {Gajewski, Herbert},
journal = {Aplikace matematiky},
keywords = {diffusion problems; iterative solution; Banach fixed-point theorem; nonlinear heat-conduction; generalized Sobolev spaces of vector valued function; Diffusion Problems; Iterative Solution; Banach Fixed-Point Theorem; Nonlinear Heat-Conduction; Generalized Sobolev Spaces of Vector Valued Function},
language = {eng},
number = {2},
pages = {77-91},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On iterative solution of nonlinear heat-conduction and diffusion problems},
url = {http://eudml.org/doc/14993},
volume = {22},
year = {1977},
}

TY - JOUR
AU - Gajewski, Herbert
TI - On iterative solution of nonlinear heat-conduction and diffusion problems
JO - Aplikace matematiky
PY - 1977
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 22
IS - 2
SP - 77
EP - 91
AB - The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.
LA - eng
KW - diffusion problems; iterative solution; Banach fixed-point theorem; nonlinear heat-conduction; generalized Sobolev spaces of vector valued function; Diffusion Problems; Iterative Solution; Banach Fixed-Point Theorem; Nonlinear Heat-Conduction; Generalized Sobolev Spaces of Vector Valued Function
UR - http://eudml.org/doc/14993
ER -

References

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  1. J. R. Cannon, A. Fasano, 10.1007/BF00735697, Arch. Rat. Mech. Anal. 53 (1973), 1 - 13. (1973) Zbl0276.35061MR0348269DOI10.1007/BF00735697
  2. H. Gajewski, K. Gröger, Ein Iterationsverfahren für Gleichungen mit einem maximal monotonen und einem stark monotonen Lipschitzstegigen Operator, Math. Nachr. 69 (1975)307-317. (1975) MR0500342
  3. H. Gajewski, K. Kröger, 10.1002/mana.19750690129, Math. Nachr. 69 (1975) 319-331. (1975) MR0513156DOI10.1002/mana.19750690129
  4. H. Gajewski, K. Gröger, 10.1002/mana.19760730119, Math. Nachr. 73 (1976) 249-267. (1976) Zbl0352.65024MR0438697DOI10.1002/mana.19760730119
  5. H. Gajewski K. Grüger K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Berlin 1974. (1974) 
  6. Y. Konishi, On the nonlinear semigroups associated with u t = Δ β ( u ) and β ( u t ) = Δ u , J. Math. Soc. Japan, 25 (1973) 622-628. (1973) MR0326517
  7. W. Strauss, Evolution equations non-linear in the time derivative, J. Math. Mech., 15 (1966) 49-82. (1966) Zbl0138.40001MR0190807

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