Error analysis of modified Runge–Kutta–Nyström methods for nonlinear second-order delay boundary value problems. (August 2023) - Zhang, Chengjian; Wang, Siyi; Tang, Changyang
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.