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Displaying 201 –
220 of
395
We consider the implicit discretization of Nagumo equation on finite lattices and show that its variational formulation corresponds in various parameter settings to convex, mountain-pass or saddle-point geometries. Consequently, we are able to derive conditions under which the implicit discretization yields multiple solutions. Interestingly, for certain parameters we show nonuniqueness for arbitrarily small discretization steps. Finally, we provide a simple example showing that the nonuniqueness...
The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.
We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the d-dimensional lattice with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector (with...
We introduce and analyze a numerical strategy
to approximate effective coefficients in stochastic homogenization of discrete elliptic
equations. In particular, we consider the simplest case possible: An elliptic equation on
the d-dimensional lattice
with independent and identically distributed conductivities on the associated edges.
Recent results by Otto and the author quantify the error made by approximating
the homogenized coefficient by the averaged energy of a regularized
corrector (with...
In this paper, we prove that the regularity property, in the sense of Gehring-Giaquinta-Modica, holds for weak solutions to non-stationary Stokes type equations. For the construction of solutions, Rothe's scheme is adopted by way of introducing variational functionals and of making use of their minimizers. Local estimates are carried out for time-discrete approximate solutions to achieve the higher integrability. These estimates for gradients do not depend on approximation.
The (modified) two-parametric Mittag-Leffler function plays an essential role in solving the so-called fractional differential equations. Its asymptotics is known (at least for a subset of its domain and special choices of the parameters). The aim of the paper is to introduce a discrete analogue of this function as a solution of a certain two-term linear fractional difference equation (involving both the Riemann-Liouville as well as the Caputo fractional -difference operators) and describe its...
This work deals with the reduction of a linear nonhomogeneous periodic system in differences (recurrence relations) to another linear non-homogeneous system with constant coefficients and an independent term. This makes it possible to study the existence and properties of periodic solutions, the asymptotic behavior and to obtain all solutions in closed form.
Currently displaying 201 –
220 of
395