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Differenzenschemata monotoner Art für schwach gekoppelte Systeme parabolischer Differentialgleichungen mit gemischten Randbedingungen. (German) Zbl 0241.65070


MSC:

65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
Full Text: DOI

References:

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[2] Collatz, L.: Funktionalanalysis und numerische Mathematik. Berlin: Springer-Verlag, 1964. · Zbl 0139.09802
[3] Douglas, J.: A survey of numerical methods for parabolic differential equations. Advances in Computers,2, 1–54 (1961). · Zbl 0133.38503 · doi:10.1016/S0065-2458(08)60140-0
[4] Gorenflo, R.: Monotonic difference schemes for weakly coupled systems of parabolic differential equations.J. Ll. Morris (editor): Conference on the numerical solution of differential equations, Dundee/Scotland 1969. Lecture Notes in Mathematics109, 160–167 (1969). · Zbl 0185.41902
[5] Gorenflo, R.: Differenzenschemata monotoner Art für lineare parabolische Randwertaufgaben. ZAMM51, 595–610 (1971). · Zbl 0244.35004 · doi:10.1002/zamm.19710510803
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[9] Krawczyk, R.: Über Differenzenverfahren bei parabolischen Differentialgleichungen. Arch. Rat. Mech. Anal.13, 81–121 (1963). · Zbl 0109.34603 · doi:10.1007/BF01262685
[10] Rose, M. E.: On the integration of non-linear parabolic equations by implicit difference methods. Quart. Appl. Math.14, 237–248 (1956/57). · Zbl 0072.14702
[11] Saulyev, V. K.: Integration of equations of parabolic type by the method of nets. Übersetzung aus dem Russischen. Oxford: Pergamon Press, 1964.
[12] Varga, R. S.: Matrix iterative analysis. Englewood Cliffs, New Jersey: Prentice Hall Inc., 1962. · Zbl 0133.08602
[13] Walter, W.: Differential- und Integral-Ungleichungen. Berlin-Göttingen-Heidelberg-New York: Springer, 1964.
[14] Fitzke, A.: On a system of difference inequalities of parabolic type. Ann. Polon. math.22, 299–302 (1970). · Zbl 0201.42201
[15] Fitzke, A.: A convergence proof of a difference scheme for a parabolic system. Ann. Polon. math.22, 317–321 (1970). · Zbl 0201.42202
[16] Kowalski, Z.: A difference method for a non-linear system of parabolic differential equations without mixed derivatives. Bull. Acad. Polon. Sci., ser. sci. math., astr. et phys.15, 683–689 (1967). · Zbl 0157.23003
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