Implicit Runge-Kutta-Nyström Methods with Lagrange Interpolation for Nonlinear Second-Order IVPs with Time-Variable Delay
Year: 2024
Author: Chengjian Zhang, Siyi Wang, Changyang Tang
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 2 : pp. 423–436
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2022-0290
Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 2 : pp. 423–436
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Nonlinear second-order initial value problems time-variable delay Lagrange interpolation implicit Runge-Kutta-Nyström methods error analysis global stability.