@phdthesis{Perera2021,
  author    = {Perera, Upeksha},
  title     = {Solutions of direct and inverse Sturm-Liouville problems},
  doi       = {10.25932/publishup-53006},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-530064},
  school      = {Universit{\"a}t Potsdam},
  pages     = {x, 109},
  year      = {2021},
  abstract  = {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 up to order eight), with a mix of boundary conditions (including non-separable and finite singular endpoints), 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. Next, a concrete implementation to the inverse Sturm-Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm-Liouville problems of order n=2,4 is verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides methods that can be adapted successfully for solving a direct (regular/singular) or inverse SLP of an arbitrary order with arbitrary boundary conditions.},
  language  = {en}
}