Convergence analysis of finite difference schemes for semi-linear initial-value problems

J. Löfström; V. Thomée

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1976)

  • Volume: 10, Issue: R2, page 61-86
  • ISSN: 0764-583X

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Löfström, J., and Thomée, V.. "Convergence analysis of finite difference schemes for semi-linear initial-value problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 10.R2 (1976): 61-86. <http://eudml.org/doc/193280>.

@article{Löfström1976,
author = {Löfström, J., Thomée, V.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
language = {eng},
number = {R2},
pages = {61-86},
publisher = {Dunod},
title = {Convergence analysis of finite difference schemes for semi-linear initial-value problems},
url = {http://eudml.org/doc/193280},
volume = {10},
year = {1976},
}

TY - JOUR
AU - Löfström, J.
AU - Thomée, V.
TI - Convergence analysis of finite difference schemes for semi-linear initial-value problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1976
PB - Dunod
VL - 10
IS - R2
SP - 61
EP - 86
LA - eng
UR - http://eudml.org/doc/193280
ER -

References

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  2. 2. R. ANSORGE and R. HASS, Konvergenz von Differenzenverfahren für lineare und nichtlineare Anfangswertaufgaben. Lecture Notes in Mathematics, n° 159, Springer-Verlag, Berlin-Heidelberg-New York, 1970. Zbl0213.11305MR292311
  3. 3. P. BRENNER, V. THOMÉE and L. B. WAHLBIN, Besov Spaces and Applications to Difference Methods for Initial Value Problems, Lecture Notes in Mathematics, n° 434, Springer-Verlag, Berlin-Heidelberg-New York, 1975. Zbl0294.35002MR461121
  4. 4. P. L. BUTZER and H. BERENS, Semi-groups of Operators and Approximation. Springer-Verlag, Berlin-Heidelberg-New York, 1967. Zbl0164.43702MR230022
  5. 5. K. JÖRGENS, Das Anfangswertproblem in Grossen für eine klasse nichtlinearer Wellengleichungen, Math. Z., Vol. 77, 1961, pp. 295-308. Zbl0111.09105MR130462
  6. 6. J.-L. LIONS, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod - Gauthier-Villars, Paris, 1969. Zbl0189.40603MR259693
  7. 7. J. LÖFSTRÖM, Besov Spaces in the Theory of Approximation, Ann. Mat. Pura Appl., Vol. 55, 1970, pp. 93-184. Zbl0193.41401MR267332
  8. 8. J. PEETRE, Espaces d'interpolation et théorème de Soboleff, Ann. Inst. Fourier, Vol. 16, 1966, pp. 279-317. Zbl0151.17903MR221282
  9. 9. PEETRE, Applications de la théorie des espaces d'interpolation dans l'analyse harmonique, Ricerche Mat., Vol. 15, 1966, pp. 1-36. Zbl0154.15302
  10. 10. J. PEETRE, Interpolation of Lipschitz Operators and Metric Spaces, Mathematica, 12, (35), No. 2, 1970, pp. 325-334. Zbl0217.44504MR482280
  11. 11. I. E . SEGAL, Non-Linear Semi-Groups, Ann. Math., 78, 1963, pp. 339-364. Zbl0204.16004MR152908
  12. 12. V. THOMÉE, Convergence Analysis of a Finite Difference Scheme for a Simple Semi-Linear Hyperbolic Equation (Numerische Behandlung nichtlinearer Integrodifferential- und Differentialgleichungen), Lecture Notes in Mathematics, n° 395, Springer-Verlag, Berlin-Heidelberg-New York, 1974, pp. 149-166. Zbl0289.65038MR356531
  13. 13. V. THOMÉE, On the Rate of Convergence of Différence Schemes for Hyperbolic Equations (Numerical Solutions of Partial Differential Equations II), Ed. B. HUBBARD, Academic Press, New York, 1971, pp. 585-622.. Zbl0237.65055

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