deval
Evaluate differential equation solution structure
Description
Examples
Evaluate DDE with Constant Delays
This example solves the DDE equation y' = ddex1de(t,y,Z)
using dde23
, then plots the solution.
Solve the system using dde23
.
sol = dde23(@ddex1de, [1 0.2], @ddex1hist, [0 5]);
Evaluate the solution at 100 points in the interval [0 5]
.
x = linspace(0,5); y = deval(sol,x);
Plot the solution.
plot(x,y)
Evaluate van der Pol Equation
This example solves the system y' = vdp1(t,y)
using ode45
, then plots the first component of the solution.
Solve the system using ode45
.
sol = ode45(@vdp1, [0 20], [2 0]);
Evaluate the first component of the solution at 100 points in the interval [0 20]
.
x = linspace(0,20,100); y = deval(sol,x,1);
Plot the solution.
plot(x,y)
Slope of Interpolating Function
Solve the simple ODE y' = t^2
with initial condition y0 = 0
in the interval using ode23
.
sol = ode23(@(t,y) t^2, [0 3], 0);
Evaluate the solution at seven points. The solution structure sol
contains an interpolating function that deval
uses to produce a continuous solution at these points. Specify a second output argument with deval
to also return the derivative of the interpolating function at the specified points.
x = linspace(0,3,7); [y,yp] = deval(sol,x)
y = 1×7
0 0.0417 0.3333 1.1250 2.6667 5.2083 9.0000
yp = 1×7
0 0.2500 1.0000 2.2500 4.0000 6.2500 9.0000
Input Arguments
sol
— Solution structure
structure
Solution structure, specified as a structure returned by one of these differential equation solvers.
Initial value problem solver —
ode45
,ode23
,ode113
,ode15s
,ode23s
,ode23t
,ode23tb
,ode15i
Delay differential equations solver —
dde23
,ddesd
, orddensd
Boundary value problem solver —
bvp4c
orbvp5c
Example: sol = ode45(@myode,tspan,y0)
Data Types: struct
x
— Evaluation points
vector
Evaluation points, specified as a vector. x
specifies
the points at which you want the value of the solution. The elements
of x
must be contained in the original integration
interval, [sol.x(1) sol.x(end)]
. For each index i
,
the solution y(:,i)
corresponds to x(i)
.
Example: 0:0.1:1
Example: [2
3 5 8]
Data Types: single
| double
idx
— Solution components to return
vector
Solution components to return, specified as a vector. Use this input when you are only interested in certain components of the solution.
Example: y = deval(sol,x,[2 3])
returns only
the second and third solution components.
Data Types: single
| double
Output Arguments
y
— Interpolated solution
vector | matrix
Interpolated solution, returned as a vector or matrix. The number
of rows in y
is equal to the number of solution
components being returned.
For multipoint boundary value problems, the solution obtained
by bvp4c
or bvp5c
might
be discontinuous at the interfaces. For an interface point xc
,
the deval
function returns the average of the
limits from the left and right of xc
. To get the
limit values, set the value of x
to be slightly
larger or smaller than xc
.
yp
— Derivative of continuous solution produced by sol
vector | matrix
Derivative of continuous solution produced by sol
,
returned as a vector or matrix. yp
is the same
size as y
and indicates the slope of the interpolating
function used by sol
at each solution point in y
.
Extended Capabilities
Thread-Based Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
Version History
Introduced before R2006a
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