@phdthesis{Pornsawad2010,
  author    = {Pornsawad, Pornsarp},
  title     = {Solution of nonlinear inverse ill-posed problems via Runge-Kutta methods},
  address   = {Potsdam},
  pages     = {104 S.},
  year      = {2010},
  language  = {en}
}
@article{PornsawadD'AmicoBoeckmannetal.2012,
  author    = {Pornsawad, Pornsarp and D'Amico, Giuseppe and B{\"o}ckmann, Christine and Amodeo, Aldo and Pappalardo, Gelsomina},
  title     = {Retrieval of aerosol extinction coefficient profiles from Raman lidar data by inversion method},
  series = {Applied optics},
  volume    = {51},
  journal   = {Applied optics},
  number    = {12},
  publisher = {Optical Society of America},
  address   = {Washington},
  issn      = {1559-128X},
  doi       = {10.1364/AO.51.002035},
  pages     = {2035 -- 2044},
  year      = {2012},
  abstract  = {We regard the problem of differentiation occurring in the retrieval of aerosol extinction coefficient profiles from inelastic Raman lidar signals by searching for a stable solution of the resulting Volterra integral equation. An algorithm based on a projection method and iterative regularization together with the L-curve method has been performed on synthetic and measured lidar signals. A strategy to choose a suitable range for the integration within the framework of the retrieval of optical properties is proposed here for the first time to our knowledge. The Monte Carlo procedure has been adapted to treat the uncertainty in the retrieval of extinction coefficients.},
  language  = {en}
}
@article{PornsawadBoeckmann2016,
  author    = {Pornsawad, Pornsarp and B{\"o}ckmann, Christine},
  title     = {Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems},
  series = {Numerical functional analysis and optimization : an international journal of rapid publication},
  volume    = {37},
  journal   = {Numerical functional analysis and optimization : an international journal of rapid publication},
  publisher = {Wiley-VCH},
  address   = {Philadelphia},
  issn      = {0163-0563},
  doi       = {10.1080/01630563.2016.1219744},
  pages     = {1562 -- 1589},
  year      = {2016},
  abstract  = {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 a Holder-type sourcewise condition if the Frechet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt, Lobatto, and Radau methods.},
  language  = {en}
}
@article{PornsawadSapsakulBoeckmann2019,
  author    = {Pornsawad, Pornsarp and Sapsakul, Nantawan and B{\"o}ckmann, Christine},
  title     = {A modified asymptotical regularization of nonlinear ill-posed problems},
  series = {Mathematics},
  volume    = {7},
  journal   = {Mathematics},
  edition   = {5},
  publisher = {MDPI},
  address   = {Basel, Schweiz},
  issn      = {2227-7390},
  doi       = {10.3390/math7050419},
  pages     = {19},
  year      = {2019},
  abstract  = {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.},
  language  = {en}
}
@article{PornsawadSungcharoenBoeckmann2020,
  author    = {Pornsawad, Pornsarp and Sungcharoen, Parada and B{\"o}ckmann, Christine},
  title     = {Convergence rate of the modified Landweber method for solving inverse potential problems},
  series = {Mathematics : open access journal},
  volume    = {8},
  journal   = {Mathematics : open access journal},
  number    = {4},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2227-7390},
  doi       = {10.3390/math8040608},
  pages     = {22},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}
@article{PornsawadBoeckmannPanitsupakamon2022,
  author    = {Pornsawad, Pornsarp and B{\"o}ckmann, Christine and Panitsupakamon, Wannapa},
  title     = {The Levenberg-Marquardt regularization for the backward heat equation with fractional derivative},
  series = {Electronic transactions on numerical analysis - ETNA},
  volume    = {57},
  journal   = {Electronic transactions on numerical analysis - ETNA},
  publisher = {Kent State University},
  address   = {Kent},
  isbn      = {978-3-7001-8258-0},
  issn      = {1068-9613},
  doi       = {10.1553/etna_vol57s67},
  pages     = {67 -- 79},
  year      = {2022},
  abstract  = {The backward heat problem with time-fractional derivative in Caputo's sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg-Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a H{\"o}lder-type source condition. Numerical examples for one and two dimensions are provided.},
  language  = {en}
}