Convergence analysis of finite difference schemes for semi-linear initial-value problems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 10 (1976) no. R2, p. 61-86
@article{M2AN_1976__10_2_61_0,
     author = {L\"ofstr\"om, J. and Thom\'ee, V.},
     title = {Convergence analysis of finite difference schemes for semi-linear initial-value problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {Dunod},
     volume = {10},
     number = {R2},
     year = {1976},
     pages = {61-86},
     zbl = {0332.35006},
     mrnumber = {488816},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1976__10_2_61_0}
}
Löfström, J.; 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, Tome 10 (1976) no. R2, pp. 61-86. http://www.numdam.org/item/M2AN_1976__10_2_61_0/

1. R. Ansorge, C. Geiger and R. Hass, Existenz und numerische Erfassbarkeit verallgemeinerter Losungen halblinearer Anfangswertaufgaben, Z. Angew. Math. Mech., Vol. 52, 1972, pp. 597-605. | MR 391525 | Zbl 0251.65060

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. | MR 292311 | Zbl 0213.11305

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. | MR 461121 | Zbl 0294.35002

4. P. L. Butzer and H. Berens, Semi-groups of Operators and Approximation. Springer-Verlag, Berlin-Heidelberg-New York, 1967. | MR 230022 | Zbl 0164.43702

5. K. Jörgens, Das Anfangswertproblem in Grossen für eine klasse nichtlinearer Wellengleichungen, Math. Z., Vol. 77, 1961, pp. 295-308. | MR 130462 | Zbl 0111.09105

6. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod - Gauthier-Villars, Paris, 1969. | MR 259693 | Zbl 0189.40603

7. J. Löfström, Besov Spaces in the Theory of Approximation, Ann. Mat. Pura Appl., Vol. 55, 1970, pp. 93-184. | MR 267332 | Zbl 0193.41401

8. J. Peetre, Espaces d'interpolation et théorème de Soboleff, Ann. Inst. Fourier, Vol. 16, 1966, pp. 279-317. | Numdam | MR 221282 | Zbl 0151.17903

9. Peetre, Applications de la théorie des espaces d'interpolation dans l'analyse harmonique, Ricerche Mat., Vol. 15, 1966, pp. 1-36. | Zbl 0154.15302

10. J. Peetre, Interpolation of Lipschitz Operators and Metric Spaces, Mathematica, 12, (35), No. 2, 1970, pp. 325-334. | MR 482280 | Zbl 0217.44504

11. I. E . Segal, Non-Linear Semi-Groups, Ann. Math., 78, 1963, pp. 339-364. | MR 152908 | Zbl 0204.16004

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. | MR 356531 | Zbl 0289.65038

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.. | Zbl 0237.65055