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In many application areas, one finds evolutionary problems with an after-effect whose numerical solution is based on the use of an integrator for ODEs combined with a suitable continuous extension. Our aim in this chapter is to survey numerical methods for solving DDEs and NDDEs based on modified ODE formulae. Special emphasis is given to continuous Runge-Kutta methods that have been used by the author. We describe, in brief, the theory of accuracy and some issues related to numerical solutions of DDEs and NDDEs.

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Continuous Runge-Kutta Methods for Delay Differential Equations

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  • 发表日期：

    2026年

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  • Fathalla A. Rihan

摘要

In many application areas, one finds evolutionary problems with an after-effect whose numerical solution is based on the use of an integrator for ODEs combined with a suitable continuous extension. Our aim in this chapter is to survey numerical methods for solving DDEs and NDDEs based on modified ODE formulae. Special emphasis is given to continuous Runge-Kutta methods that have been used by the author. We describe, in brief, the theory of accuracy and some issues related to numerical solutions of DDEs and NDDEs.