Block generalized Störmer-Cowell methods applied to second order nonlinear delay differential equations

Li, Cui; Zhou, Yongtao

doi:10.1016/j.apnum.2022.04.005

Cited by 2 publications

(1 citation statement)

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“…Hence, in the recent years, ones have begun to develop various numerical methods to solve this kind of problems. For example, Papageorgiou & Famelis [3] constructed explicit Runge-Kutta-Nystr öm methods, Martín & García [4] presented variable-stepsize multistep methods, Ramadan, El-Sherbeiny & Sherif [5] proposed polynomial spline methods, Seong & Majid [6] gave an Adams-Moulton-type method, Kherd, Omar, Saaban & Adeyeye [7] suggested operational matrix methods, Zhang& Wang [8] derived generalized Str ömer-Cowell methods and Li & Zhou [9] further adapted the methods in [8] into block generalized Str ömer-Cowell methods.…”

Section: Introductionmentioning

confidence: 99%

Implicit Runge-Kutta-Nyström Methods with Lagrange Interpolation for Nonlinear Second-Order IVPs with Time-Variable Delay

Chengjian Zhang,

Siyi Wang,

Changyang Tang

2024

AAMM

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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-Nystr öm (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 O(h min{p,µ+ν+1} ), where p is the consistency order of the method and µ,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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