@article{OsterlohBoeckmannNicolaeetal.2013,
  author    = {Osterloh, Lukas and B{\"o}ckmann, Christine and Nicolae, Doina and Nemuc, Anca},
  title     = {Regularized inversion of microphysical atmospheric particle parameters - theory and application},
  series = {Journal of computational physics},
  volume    = {237},
  journal   = {Journal of computational physics},
  number    = {11},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0021-9991},
  doi       = {10.1016/j.jcp.2012.11.040},
  pages     = {79 -- 94},
  year      = {2013},
  abstract  = {Retrieving the distribution of aerosols in the atmosphere via remote sensing techniques is a highly complex task that requires dealing with a wide range of different problems stemming both from Physics and Mathematics. We focus on retrieving this distribution from multi-wavelength lidar data for aerosol ensembles consisting of spherical particles via an iterative regularization technique. The optical efficiencies for spherical scatterers are examined to account for the behavior of the underlying integral equation. The ill-posedness of the problem and the conditioning of the discretized problem are analyzed. Some critical points in the model, like the assumed wavelength-independence of the refractive index and the fixed grid of investigated refractive indices, are studied with regard to their expected impact on the regularized solution. A new Monte-Carlo type method is proposed for retrieval of the refractive index. To validate the results, the developed algorithm is applied to two measurement cases of burning biomass gained from multi-wavelength Raman lidar.},
  language  = {en}
}
@article{RattanaBoeckmann2013,
  author    = {Rattana, Amornrat and B{\"o}ckmann, Christine},
  title     = {Matrix methods for computing eigenvalues of Sturm-Liouville problems of order four},
  series = {Journal of computational and applied mathematics},
  volume    = {249},
  journal   = {Journal of computational and applied mathematics},
  number    = {8},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0377-0427},
  doi       = {10.1016/j.cam.2013.02.024},
  pages     = {144 -- 156},
  year      = {2013},
  abstract  = {This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions. Furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's methods as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods is investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.},
  language  = {en}
}