Solving DDE Problems
This section uses an example to describe:
dde23to solve initial value problems (IVPs) for delay differential equations (DDEs)
Example: A Straightforward Problem
This example illustrates the straightforward formulation, computation, and display of the solution of a system of DDEs with constant delays. The history is constant, which is often the case. The differential equations are
The example solves the equations on [0,5] with history
The demo |
dde23, you must rewrite the equations as an equivalent system of first-order differential equations. Do this just as you would when solving IVPs and BVPs for ODEs (see Examples: Solving Explicit ODE Problems). However, this example needs no such preparation because it already has the form of a first-order system of equations.
dde23as a vector. For the example we could use
dde23with the functions
dde23returns the mesh it selects and the solution there as fields in the solution structure
sol. Often, these provide a smooth graph.
Evaluating the Solution at Specific Points
The method implemented in
dde23 produces a continuous solution over the whole interval of integration . You can evaluate the approximate solution, , at any point in using the helper function
deval and the structure
sol returned by
deval function is vectorized. For a vector
ith column of
Sint approximates the solution .
Using the output
sol from the previous example, this code evaluates the numerical solution at 100 equally spaced points in the interval [0,5] and plots the result.
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