论文标题
delaydiffeq：通过递归嵌入普通微分方程求解器生成延迟微分方程求解器
DelayDiffEq: Generating Delay Differential Equation Solvers via Recursive Embedding of Ordinary Differential Equation Solvers
论文作者
论文摘要
传统的用于延迟微分方程（DDE）的求解器仅围绕一种方法设计，并且没有有效地使用其更发达的普通微分方程（ODE）对应物的基础架构。在这项工作中，我们介绍了DelastDiffeq，这是一种用于求解延迟微分方程（DDES）的朱利娅包装，该方程利用了普通脱衣机中的多种数值算法来求解刚性和非验证odes，并设法求解了挑战性的刚性僵硬的DDE。我们描述了如何在自身内部编译ode积分器，并考虑不连续传播的情况，这将导致一种对DDE有效的设计，同时使用所有ODE内部。我们重点介绍了数值DDE求解器必须解决的一些困难，并解释了delaydiffq如何处理这些问题。我们展示了delaydiffeq如何能够求解困难方程，其硬度DDE求解器如何在时间尺度分离的问题上效率，以及该设计如何允许用法中的通用性和灵活性，例如重新使用以生成用于随机延迟差分方程的求解器。
Traditional solvers for delay differential equations (DDEs) are designed around only a single method and do not effectively use the infrastructure of their more-developed ordinary differential equation (ODE) counterparts. In this work we present DelayDiffEq, a Julia package for numerically solving delay differential equations (DDEs) which leverages the multitude of numerical algorithms in OrdinaryDiffEq for solving both stiff and non-stiff ODEs, and manages to solve challenging stiff DDEs. We describe how compiling the ODE integrator within itself, and accounting for discontinuity propagation, leads to a design that is effective for DDEs while using all of the ODE internals. We highlight some difficulties that a numerical DDE solver has to address, and explain how DelayDiffEq deals with these problems. We show how DelayDiffEq is able to solve difficult equations, how its stiff DDE solvers give efficiency on problems with time-scale separation, and how the design allows for generality and flexibility in usage such as being repurposed for generating solvers for stochastic delay differential equations.
