Adapted Runge-Kutta Methods for Nonlinear First-Order Delay BVPs with Time-variable Delay  

作　　者：Cheng-jian ZHANG Yang WANG Hao HAN 

机构地区：[1]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China [2]Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期400-413,共14页应用数学学报(英文版)

基　　金：supported by the National Natural Science Foundation of China(Grant No.12471379).

摘　　要：This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs)with time-variable delay.For solving this kind of delay BVPs,by combining Runge-Kutta methods with Lagrange interpolation,a class of adapted Runge-Kutta(ARK)methods are developed.Under the suitable conditions,it is proved that ARK methods are convergent of order minfp;++1g,where p is the consistency order of ARK methods and;are two given parameters in Lagrange interpolation.Moreover,a global stability criterion is derived for ARK methods.With some numerical experiments,the computational accuracy and global stability of ARK methods are further testified.

关 键 词：delay boundary value problems adapted Runge-Kutta method Lagrange interpolation error analysis global stability 

分 类 号：O241.8[理学—计算数学]