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Now showing items 61-64 of 64
Preprint
Functions satisfying holonomic q-differential equations
(2007-05-21)
In a similar manner as in some previous papers, where explicit algorithms for finding the differential equations satisfied by holonomic functions were given, in this paper we deal with the space of the q-holonomic functions which are the solutions of linear q-differential equations with polynomial coefficients. The sum, product and the composition with power functions of q-holonomic functions are also q-holonomic and the resulting q-differential equations can be computed algorithmically.
Preprint
On the Computation of Fourier Coefficients
(2006-11-16)
In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f'(t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f'(t) are known, and vice versa. Furthermore this generates an iterative scheme for N times differentiable functions complementing the direct computation of Fourier coefficients via the defining integrals which can be also treated automatically in certain cases.
Preprint
Balanced Viscosity solutions to a rate-independent system for damage
(2017-05-02)
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems. While in the first two papers [KRZ13, KRZ15] the assumptions on the spatial domain $\Omega$ were kept as general as possible (i.e. nonsmooth domain with mixed boundary conditions), we assume here that $\partial\Omega$ is smooth and that the type of boundary conditions does not change. This smoother setting allows us to derive enhanced regularity spatial properties both for the ...
Preprint
Numerical Methods for Non-Stationary Stokes Flow
(2008)
We consider a first order implicit time stepping procedure (Euler scheme) for the non-stationary Stokes equations in smoothly bounded domains of R3. Using energy estimates we can prove optimal convergence properties in the Sobolev spaces Hm(G) (m = 0;1;2) uniformly in time, provided that the solution of the Stokes equations has a certain degree of regularity. For the solution of the resulting Stokes resolvent boundary value problems we use a representation in form of hydrodynamical volume and boundary layer potentials, ...