TY  - GEN
A1  - Perera, Upeksha
A1  - Böckmann, Christine
T1  - Solutions of direct and inverse even-order Sturm-Liouville problems using Magnus expansion
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1336 
KW  - higher-order Sturm–Liouville problems
KW  - inverse Sturm–Liouville problems
KW  - Magnus expansion
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473414
SN  - 1866-8372
IS  - 1336
ER  - 
TY  - GEN
A1  - Pornsawad, Pornsarp
A1  - Sapsakul, Nantawan
A1  - Böckmann, Christine
T1  - A modified asymptotical regularization of nonlinear ill-posed problems
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we investigate the continuous version of modified iterative Runge–Kutta-type methods for nonlinear inverse ill-posed problems proposed in a previous work. The convergence analysis is proved under the tangential cone condition, a modified discrepancy principle, i.e., the stopping time T is a solution of ∥𝐹(𝑥𝛿(𝑇))−𝑦𝛿∥=𝜏𝛿+ for some 𝛿+>𝛿, and an appropriate source condition. We yield the optimal rate of convergence.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1335 
KW  - nonlinear operator
KW  - regularization
KW  - discrepancy principle
KW  - asymptotic method
KW  - optimal rate
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-473433
SN  - 1866-8372
IS  - 1335
ER  - 
TY  - GEN
A1  - Pornsawad, Pornsarp
A1  - Sungcharoen, Parada
A1  - Böckmann, Christine
T1  - Convergence rate of the modified Landweber method for solving inverse potential problems
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - In this paper, we present the convergence rate analysis of the modified Landweber method under logarithmic source condition for nonlinear ill-posed problems. The regularization parameter is chosen according to the discrepancy principle. The reconstructions of the shape of an unknown domain for an inverse potential problem by using the modified Landweber method are exhibited.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1034 
KW  - nonlinear operator
KW  - regularization
KW  - modified Landweber method
KW  - discrepancy principle
KW  - logarithmic source condition
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-471942
SN  - 1866-8372
IS  - 1034
ER  -