Abstract
Differential equations with discrete and distributed delays are considered. Explicit continuous-stage Runge–Kutta methods for state-dependent discrete delays based on functional continuous methods for retarded functional differential equations and Runge–Kutta methods for integro-differential equations based on methods for Volterra equations are combined to get a method suitable for both types of delays converging with order four. A method that requires six right-hand side evaluations and only two of its integral argument evaluations is presented. The questions of the practical implementation for delay differential equations within general non-smooth solutions are discussed. The numerical solution of test problems confirms the declared fourth order of convergence of the constructed method.
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Eremin, A.S., Lobaskin, A.A. (2022). Fourth-Order Method for Differential Equations with Discrete and Distributed Delays. In: Smirnov, N., Golovkina, A. (eds) Stability and Control Processes. SCP 2020. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-87966-2_21
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DOI: https://doi.org/10.1007/978-3-030-87966-2_21
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