Abstract
The properties of contractivity, monotonicity, and sign constancy of approximate methods of solution of the initial problem are studied for linear and nonlinear differential operator equations in a complex Hilbert space. Explicit methods of first and second order of accuracy are presented that are monotonc and sign constant in the corresponding classes of problems for any value of the mesh size.
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K. Decker and J. Werber, Stability of Runge-Kutta Methods for Rigid Nonlinear Differential Equations [Russian translation], Mir, Moscow (1988).
P. I. Bodnarchuk and Ya. N. Glinskii, “On proving certain nonlinear numerical methods of solution of ordinary differential equations,” Deposited at VINITI, No. 4155-85 Dep., Minsk (1985).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1593–1598, December, 1990.
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Glins'kii, Y.M. Uniformly monotonic explicit approximate methods for first-order differential operator equations in Hilbert space. Ukr Math J 42, 1430–1435 (1990). https://doi.org/10.1007/BF01060812
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DOI: https://doi.org/10.1007/BF01060812