Methods Based on Polynomial Chaos for Quadratic Delay Differential Equations With Random Parameters

Key Points

The investigation finds that using polynomial chaos methods enhances solution representation of delay differential equations.
Key findings indicate the stochastic Galerkin method successfully computes coefficient functions in 2 case studies.
Assessment using stochastic collocation techniques enables effective uncertainty quantification of the system.
This approach highlights that stationary solutions' stability may vary based on the chosen numerical methods.

Abstract

ABSTRACT We consider systems of delay differential equations (DDEs), including a single delay and a quadratic right‐hand side. In a system, parameters are replaced by random variables to perform an uncertainty quantification. Thus the solution of the DDEs becomes a random process, which can be represented by a series of the generalised polynomial chaos. We investigate the application of the stochastic Galerkin method and stochastic collocation techniques to compute unknown coefficient functions of the series. Furthermore, existence and local stability of stationary solutions are discussed for each type of method. We present results of numerical computations in two illustrative examples: a logistic equation and an epidemiological model.

Methods Based on Polynomial Chaos for Quadratic Delay Differential Equations With Random Parameters

Key Points

Abstract

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