TY - JOUR
T1 - Implicit Runge-Kutta-Nyström Methods with Lagrange Interpolation for Nonlinear Second-Order IVPs with Time-Variable Delay
AU - Zhang , Chengjian
AU - Wang , Siyi
AU - Tang , Changyang
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 423
EP - 436
PY - 2024
DA - 2024/01
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2022-0290
UR - https://global-sci.org/intro/article_detail/aamm/22338.html
KW - Nonlinear second-order initial value problems, time-variable delay, Lagrange interpolation, implicit Runge-Kutta-Nyström methods, error analysis, global stability.
AB - <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>