Adv. Appl. Math. Mech., 16 (2024), pp. 423-436.
Published online: 2024-01
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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.
}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0290}, url = {http://global-sci.org/intro/article_detail/aamm/22338.html} }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.