TY  - INPR
A1  - Pornsawad, Pornsarp
A1  - Böckmann, Christine
T1  - Modified iterative Runge-Kutta-type methods for nonlinear ill-posed problems
N2  - This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under Hölder-type source-wise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt and Radau methods.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 7 
KW  - ill-posed problems
KW  - Runge-Kutta methods
KW  - regularization methods
KW  - Hölder-type source condition
KW  - stopping rules
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70834
SN  - 2193-6943
VL  - 3
IS  - 7
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Chang, Der-Chen
A1  - Habal, Nadia
A1  - Schulze, Bert-Wolfgang
T1  - The edge algebra structure of the Zaremba problem
JF  - Journal of pseudo-differential operators and applications
N2  - We study mixed boundary value problems, here mainly of Zaremba type for the Laplacian within an edge algebra of boundary value problems. The edge here is the interface of the jump from the Dirichlet to the Neumann condition. In contrast to earlier descriptions of mixed problems within such an edge calculus, cf. (Harutjunjan and Schulze, Elliptic mixed, transmission and singular crack problems, 2008), we focus on new Mellin edge quantisations of the Dirichlet-to-Neumann operator on the Neumann side of the boundary and employ a pseudo-differential calculus of corresponding boundary value problems without the transmission property at the interface. This allows us to construct parametrices for the original mixed problem in a new and transparent way.
Y1  - 2014
U6  - https://doi.org/10.1007/s11868-013-0088-7
SN  - 1662-9981
SN  - 1662-999X
VL  - 5
IS  - 1
SP  - 69
EP  - 155
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Schulze, Bert-Wolfgang
A1  - Wei, Y.
T1  - The Mellin-edge quantisation for corner operators
JF  - Complex analysis and operator theory
N2  - We establish a quantisation of corner-degenerate symbols, here called Mellin-edge quantisation, on a manifold with second order singularities. The typical ingredients come from the "most singular" stratum of which is a second order edge where the infinite transversal cone has a base that is itself a manifold with smooth edge. The resulting operator-valued amplitude functions on the second order edge are formulated purely in terms of Mellin symbols taking values in the edge algebra over . In this respect our result is formally analogous to a quantisation rule of (Osaka J. Math. 37:221-260, 2000) for the simpler case of edge-degenerate symbols that corresponds to the singularity order 1. However, from the singularity order 2 on there appear new substantial difficulties for the first time, partly caused by the edge singularities of the cone over that tend to infinity.
Y1  - 2014
U6  - https://doi.org/10.1007/s11785-013-0289-3
SN  - 1661-8254
SN  - 1661-8262
VL  - 8
IS  - 4
SP  - 803
EP  - 841
PB  - Springer
CY  - Basel
ER  - 
TY  - CHAP
A1  - Andersson, H.
A1  - Keunecke, A.
A1  - Eser, A.
A1  - Huisinga, Wilhelm
A1  - Reinisch, W.
A1  - Kloft, Charlotte
T1  - Pharmacokinetic considerations for optimising dosing regimens of  a potsdam univ infliximab in patients with Crohn's disease
T2  - JOURNAL OF CROHNS & COLITIS
Y1  - 2014
U6  - https://doi.org/10.1016/S1873-9946(14)60086-6
SN  - 1873-9946
SN  - 1876-4479
VL  - 8
SP  - S44
EP  - S44
PB  - Oxford Univ. Press
CY  - Oxford
ER  -