@Article{AAMM-16-2,
author = {Zhang, Chengjian and Wang, Siyi and Tang, Changyang},
title = {Implicit Runge-Kutta-Nyström Methods with Lagrange Interpolation for Nonlinear Second-Order IVPs with Time-Variable Delay},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {16},
number = {2},
pages = {423--436},
abstract = {<p style="text-align: justify;">This paper deals with nonlinear second-order initial value problems with
time-variable delay. For solving this kind of problems, a class of implicit Runge-Kutta-Nyström (IRKN) methods with Lagrange interpolation are suggested. Under the suitable condition, it is proved that an IRKN method is globally stable and has the computational accuracy $\mathcal{O}(h^{min\{p,\mu+ν+1\}}),$ where $p$ is the consistency order of the method
and $\mu, ν ≥0$ are the interpolation parameters. Combining a fourth-order compact difference scheme with IRKN methods, an initial-boundary value problem of nonlinear
delay wave equations is solved. The presented experiments further confirm the computational effectiveness of the methods and the theoretical results derived in previous.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0290},
url = {https://global-sci.com/article/72816/implicit-runge-kutta-nystrom-methods-with-lagrange-interpolation-for-nonlinear-second-order-ivps-with-time-variable-delay}
}