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.

Original languageEnglish
Pages (from-to)165-181
Number of pages17
JournalApplied Numerical Mathematics
Volume146
Early online date10 Jul 2019
DOIs
StatePublished - 1 Dec 2019

    Research areas

  • Continuous Runge–Kutta, Delay differential equations, Functional differential equations, Overlapping, NUMERICAL-SOLUTION, Continuous Runge-Kutta

    Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Numerical Analysis

ID: 43756490