Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

A three operator split-step method covering a larger set of non-linear partial differential equations


Zia,  Haider
Miller Group, Atomically Resolved Dynamics Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

External Resource
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

(Preprint), 938KB

Supplementary Material (public)
There is no public supplementary material available

Zia, H. (2017). A three operator split-step method covering a larger set of non-linear partial differential equations. Communications in Nonlinear Science and Numerical Simulation, 47, 277-291. doi:10.1016/j.cnsns.2016.11.020.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-5F34-6
This paper describes an updated Fourier based split-step method that can be applied to a greater class of partial differential equations, than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized non-linear Schr\"odinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.