Year 2023

• Effective highly accurate time integrators for linear Klein-Gordon equations across the scales

  Publication

  • K. Lademann
  • K. Kropielnicka
  • K. Schratz

  - Year 2023

  We propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant...

• THIRD-ORDER EXPONENTIAL INTEGRATOR FOR LINEAR KLEIN–GORDON EQUATIONS WITH TIME AND SPACE-DEPENDANT MASS

  Publication

  • K. Lademann
  • K. Kropielnicka

  - Year 2023

  Allowing for space- and time-dependance of mass in Klein–Gordon equations re- solves the problem of negative probability density and of violation of Lorenz covariance of interaction in quantum mechanics. Moreover it extends their applicability to the domain of quantum cosmology, where the variation in mass may be accompanied by high oscillations....

Year 2019

• On the Matano Plane Position in Multicomponent Diffusion Couples

  Publication

  • K. Lademann
  • H. Leszczyński
  • K. Tkacz-Śmiech
  • B. Bożek
  • M. Zajusz
  • M. Danielewski

  - Nano Hybrids and Composites - Year 2019

  Even though several methods of diffusion analysis avoid a necessity for the Matano plane determination, the Matano plane locations are of interest in the multicomponent couples and when tracer experiments are performed. The positions of the Matano plane calculated from the concentration profiles should be exactly the same. However, due to experimental errors, the results can differ significantly. In the paper we consider Matano...