Compact difference schemes for weakly-nonlinear parabolic and Schrodinger-type equations and systems
Mathematical Physics
2018-12-31 v2 math.MP
Numerical Analysis
Abstract
The implicit compact finite-difference scheme was developed for evolutionary partial differential parabolic and Schr\"odinger-type equations and systems with a weak nonlinearity. To make a temporal step of the compact implicit scheme we need to solve a non-linear system. We use for this step a simple explicit difference scheme and then Newton -- Raphson iterations, which are implemented by the double-sweep method. Numerical experiments confirm the 4-th order of an algorithm. The Richardson extrapolation improves it up to the 6-th order.
Cite
@article{arxiv.1712.05185,
title = {Compact difference schemes for weakly-nonlinear parabolic and Schrodinger-type equations and systems},
author = {Vladimir Gordin and Evgenii Tsymbalov},
journal= {arXiv preprint arXiv:1712.05185},
year = {2018}
}