Error analysis of modified Runge-Kutta-Nystrom methods for nonlinear second-order delay boundary value problems

This paper is concerned with the numerical solutions of nonlinear second-order boundary value problems with time-variable delay. By adapting Runge-Kutta- Nystrom (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.(c) 2023 Elsevier Ltd. All rights reserved.