2018/06/22 by Alexey S. Eremin, Eremin, Alexey S.
Engineering · Mathematics · #65L03 #65L06 #Differential Equations and Numerical Methods #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1806.08644
openalex publication_date 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the paper explicit functional continuous Runge-Kutta and Runge-Kutta-Nyström methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the special form are constructed with the reuse of the last stage of the step. The order conditions for Runge-Kutta-Nyström methods are derived. Methods of orders three, four and five which require less computations than the known methods are presented. Numerical solution of the test problems confirm the convergence order of the new methods and their lower computational cost is performed.