MATLAB Mathematics - SERC - Index of

5 Differential Equations
dde23 produces a solution that is continuous on [ t 0 , t f ]. You can use the
function deval and the output of dde23 to evaluate the solution at specific
points on the interval of integration.
dde23 tracks discontinuities and integrates the differential equations with the
explicit Runge-Kutta (2,3) pair and interpolant used by ode23. The
Runge-Kutta formulas are implicit for step sizes longer than the delays. When
the solution is smooth enough that steps this big are justified, the implicit
formulas are evaluated by a predictor-corrector iteration.
DDE Solver Basic Syntax
The basic syntax of the DDE solver is
sol = dde23(ddefun,lags,history,tspan,options)
The input arguments are
ddefun
Handle to a function that evaluates the right side of the
differential equations. The function must have the form
dydt = ddefun(t,y,Z)
where the scalar t is the independent variable, the column
vector y is the dependent variable, and Z(:,j) is yt ( – τ j ) for
τ j = lags(j). See “Function Handles” in the MATLAB
Programming documentation for more information.
lags A vector of constant positive delays τ 1 , …,
τ k .
history Handle to a function of t that evaluates the solution y()
t for
t ≤ t 0 . The function must be of the form
S = history(t)
where S is a column vector. Alternatively, if yt () is constant,
you can specify history as this constant vector.
If the current call to dde23 continues a previous integration to
t0, use the solution sol from that call as the history.
tspan
The interval of integration as a two-element vector [t0,tf]
with t0 < tf.
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