Error analysis of modified Runge–Kutta–Nyström methods for nonlinear second-order delay boundary value problems. (August 2023)

• Record Type: Journal Article
• Authors: Zhang, Chengjian; Wang, Siyi; Tang, Changyang
• Is Part Of: Applied mathematics letters. Volume 142(2023)
• Publication Date: 2023-08
• Subjects: Second-order boundary value problems -- Time-variable delay -- Modified Runge–Kutta–Nyström methods -- Error analysis; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2023.108658
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This paper is concerned with the numerical solutions of nonlinear second-order boundary value problems with time-variable delay. By adapting Runge–Kutta–Nyström (RKN) methods and combining Lagrange interpolation, a class of modified RKN (MRKN) methods are suggested for solving the problems. Under some suitable conditions, MRKN methods are proved to be convergent of order min { p, q }, where p, q are the local orders of MRKN methods and Lagrange interpolation, respectively. Numerical experiments further confirm the computational effectiveness and accuracy of MRKN methods.