Titlebook: Delay Differential Equations and Applications to Biology; Fathalla A. Rihan Book 2021 The Editor(s) (if applicable) and The Author(s), und

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https://doi.org/10.1007/978-981-16-0626-7delay differential equations; stability; Lyapunov functional; continuous RK methods; time-delays; mathema

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978-981-16-0628-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapor

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Numerical Solutions of Delay Differential Equations 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 accura

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Numerical Solutions of Volterra Delay Integro-Differential Equationsge-Kutta method and collocation method for the integral part. In the following pages, the efficiency and stability properties of this technique are examined. Later, numerical results are presented to demonstrate the effectiveness of the methodology.

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Sensitivity Analysis of Delay Differential Equationsle parameters (e.g., control functions) .(.). It is often desirable to have information about the effect on the solution of the dynamic system of perturbing the initial data, control functions, time-lags, and other parameters appearing in the model.

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Stochastic Delay Differential Equationsis an increasing need to extend the deterministic models to models that embrace more complex variations in the dynamics. A way of modeling these elements is by including stochastic influences or noise. A natural extension of a deterministic differential equations model is a system of stochastic diff