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The method of lines for nonlinear parabolic differential equations with mixed derivatives. (English) Zbl 0387.65060


MSC:

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
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References:

[1] Beckenbach, E.F., Bellman, R.: Inequalities. Berlin, Göttingen, Heidelberg: Springer 1961
[2] Fitzke, A.: Method of difference inequalities for parabolic equations with mixed derivatives. Ann. Polon. MathXXXI, 121-129 (1975) · Zbl 0335.65047
[3] Malec, M.: Methode des différences finies pour une équation différentielle partielle avec derivées mixtes. Bull. Acad. Polon. Sci. Sér. des Sci. Math. Astronom. Phys.12, 561-567 (1974) · Zbl 0283.35003
[4] Malec, M.: Système d’inegalités aux différences finies du type parabolique et applications. Collect. Math.XXXV, 305-312 (1976) · Zbl 0381.65051
[5] Motzkin, T.S., Wasow, W.: On the approximation of linear elliptic differential equations by difference equations with positive coefficients. J. Mathematical Phys.31, 253-259 (1953) · Zbl 0050.12501
[6] Ostrowski, A.: Über die Determinanten mit überwiegender Hauptdiagonale. Comment. Math. Helv.10, 69-96 (1937-38) · JFM 63.0035.01 · doi:10.1007/BF01214284
[7] Schleinkofer, G.: Approximation der Lösungen parabolischer Differentialgleichungen mit der Linienmethode. Universität Mainz (1972) Manuskript
[8] Walter, W.: Die Linienmethode bei nichtlinearen parabolischen Differentialgleichungen. Numer. Math.12, 307-321 (1968) · Zbl 0191.16902 · doi:10.1007/BF02162511
[9] Walter, W.: Differential and integral inequalities. Berlin, Heidelberg, New York: Springer 1970 · Zbl 0252.35005
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