Delay differential equation solvers
DelayDiffEq solves delay differential equations by reducing successive time intervals to ordinary differential equation solves.
DelayDiffEq.MethodOfSteps — Type
MethodOfSteps(alg; constrained = false, fpsolve = NLFunctional())Construct an algorithm that solves delay differential equations by the method of steps, where alg is an ODE algorithm from OrdinaryDiffEq.jl upon which the calculation of steps is based.
If the algorithm is constrained only steps of size at most the minimal delay will be taken. If it is unconstrained, fixed-point iteration fpsolve is applied for step sizes that exceed the minimal delay.
Citations:
General Approach
Zivari-Piran, Hossein, and Wayne H. Enright. "An efficient unified approach for the numerical solution of delay differential equations." Numerical Algorithms 53.2-3 (2010): 397-417.
State-Dependent Delays
S. P. Corwin, D. Sarafyan and S. Thompson in "DKLAG6: a code based on continuously embedded sixth-order Runge-Kutta methods for the solution of state-dependent functional differential equations", Applied Numerical Mathematics, 1997.
DelayDiffEq.Discontinuity — Type
Discontinuity(t, order)Object of discontinuity of order order at time t, i.e. discontinuity of orderth derivative at time t.