Delay differential equations contain terms whose value depends on the solution at prior times. The time delays can be constant, time-dependent, or state-dependent, and the choice of the solver function (dde23,ddesd, orddensd) depends on the type of delays in the equation. Typically the time...
By using the dense output, the solution can be computed at any time point the solver has passed to the same accuracy as the solution itself. This sidesteps the interpolation problem at the cost of a bit more book-keeping.To store the history without using ever-growing (or just huge) ...
In this paper we propose a new framework for designing a delay differential equation (DDE) solver which works with any supplied initial value problem (IVP) solver that is based on a standard step-by-step approach, such as Runge-Kutta or linear multi-step methods, and can provide dense ...
A delay differential equation solver based on a continuous Runge–Kutta method with defect control 来自 Springer 喜欢 0 阅读量: 95 作者:WH Enright,H Hayashi 摘要: We have recently developed a generic approach for solving neutral delay differential equations based on the use of a continuous Runge...
A delay differential equation is a differential equation where the time derivatives at the current time depend on the solution and possibly its derivatives at previous times: Instead of a simple initial condition, an initial history function \[Phi](t) ne
Scipy-based delay differential equation (DDE) solver. See the docstrings and examples for more infos. Examples frompylabimportcos,linspace,subplotsfromddeintimportddeint# We solve the following system:# Y(t) = 1 for t < 0# dY/dt = -Y(t - 3cos(t)**2) for t > 0defvalues_before_ze...
This paper introduces a new class of numerical delay-differential equation solvers based on state quantization instead of time slicing. The numerical properties of these algorithms, i.e., stability and convergence, are discussed, and a number of benchmark problems are being simulated and compared wi...
We present three different equations: one real-valued equation using a direct linear system solver, one complex valued equation using a direct linear system solver, and one Jacobi–Davidson style correction equation that is suitable for an iterative linear system solver. We show numerical examples ...
delay differential equation (DDE) models, both analytically and numerically. We find many broadly applicable results, including parameter reduction versus canonical ordinary differential equation (ODE) models, analytical relations for converting between ODE and DDE models, criteria for when delays may be ...
The popular MATLAB-based dde23 solver developed by Shampine and Thompson for delay differential equa- tions is well tested and user-friendly. Interested readers can fi nd many familiar and informative examples at the website http://.radford.edu/thompson/webddes/ ddetutwhite.html, and more...