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Displaying 221 –
240 of
286
In this paper we derive a posteriori error estimates for the
heat equation. The time discretization
strategy is based on a θ-method and the mesh used for each
time-slab is independent of the mesh used for the previous
time-slab. The novelty of this paper is an upper bound for the
error caused by the coarsening of the mesh used for computing the
solution in the previous time-slab. The technique applied for
deriving this upper bound is independent of the problem and can be
generalized to other time...
The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space for when the initial condition is not regular.
Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly...
First, a result of J. W. Schmidt about the monotone enclosure of solutions of nonlinear equations is generalized. Then an iteration method is considered, which is more effective than other known methods. For this method, monotone enclosure statements are also proved.
The general iteration method for nonexpansive mappings on a Banach
space is considered. Under some assumption of fast enough convergence on the
sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic
method is τ−convergent for a suitable topology τ weaker than the norm topology,
then the perturbed method is also τ−convergent. Application is presented to the
gradient-prox method for monotone inclusions in Hilbert spaces.
2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps [13] and Hölder type conditions introduced by us in [2] for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in [11].
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