Geodesic
Continuous method of second order with constant coefficients for equations of monotone type
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 1, pp. 39-45

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Convergence of the second order continuous method with constant coefficients for nonlinear equations is investigated. The cases of a monotone operator equation in Hilbert space and of an accretive operator equation in reflexive Banach space which is strictly convex together with its conjugate, are considered separately. In each case, sufficient conditions for the convergence with respect to the norm of the space specified by the method are obtained. In the accretive case, sufficient conditions for the continuous method convergence include not only the requirements on the operator equation and on the coefficients of the differential equation defining the method, but also on the geometry of space where the equation is solved. Examples of Banach spaces with the desired geometric properties are shown.
Keywords: Hilbert space, Banach space, strongly monotone operator, Lipschitz condition, strongly accretive operator, duality mapping, continuous method
Mots-clés : convergence. 
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     author = {I. P. Ryazantseva and Bubnova O.Y.},
     title = {Continuous  method of second order   with constant coefficients for equations of monotone type},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {39--45},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2018_20_1_a3/}
}
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I. P. Ryazantseva; Bubnova O.Y. Continuous  method of second order   with constant coefficients for equations of monotone type. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 20 (2018) no. 1, pp. 39-45. http://geodesic.mathdoc.fr/item/SVMO_2018_20_1_a3/