Ruprecht, DanielDanielRuprechtSchädle, AchimAchimSchädleSchmidt, FrankFrankSchmidtZschiedrich, LinLinZschiedrich2020-08-172020-08-172008-07-02SIAM Journal on Scientific Computing 5 (30): 2358-2385 (2007)http://hdl.handle.net/11420/7065A new approach to derive transparent boundary conditions (TBCs) for dispersive wave, Schrödinger, heat, and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physically reasonable and unreasonable solutions by the location of the singularities of the Laplace transform of the exterior solution. Here the Laplace transform is taken with respect to a generalized radial variable. To obtain a numerical algorithm, a Möbius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients. © 2008 Society for Industrial and Applied Mathematics.en1095-71972008523582385SIAMDrift-diffusion equationKlein-gordon equationNonreflecting boundary conditionPole conditionSchrödinger equationTransparent boundary conditionWave equationMathematikJournal Article10.1137/070692637Other