bvpset
Create or alter options structure of boundary value problem
Syntax
options = bvpset('name1',value1,'name2',value2,...)
options = bvpset(oldopts,'name1',value1,...)
options = bvpset(oldopts,newopts)
bvpset
Description
options = bvpset('name1',value1,'name2',value2,...)
creates
a structure options
that you can supply to the
boundary value problem solver bvp4c
,
in which the named properties have the specified values. Any unspecified
properties retain their default values. For all properties, it is
sufficient to type only the leading characters that uniquely identify
the property. bvpset
ignores case for property
names.
options = bvpset(oldopts,'name1',value1,...)
alters
an existing options structure oldopts
. This overwrites
any values in oldopts
that are specified using
name/value pairs and returns the modified structure as the output
argument.
options = bvpset(oldopts,newopts)
combines
an existing options structure oldopts
with a new
options structure newopts
. Any values set in newopts
overwrite
the corresponding values in oldopts
.
bvpset
with no input arguments
displays all property names and their possible values, indicating
defaults with braces {}
.
You can use the function bvpget
to
query the options
structure for the value of a
specific property.
BVP Properties
bvpset
enables you to specify properties
for the boundary value problem solver bvp4c
.
There are several categories of properties that you can set:
Error Tolerance Properties
Because bvp4c
uses a
collocation formula, the numerical solution is based on a mesh of
points at which the collocation equations are satisfied. Mesh selection
and error control are based on the residual of this solution, such
that the computed solution S(x)
is the exact solution of a perturbed problem S′(x)
= f(x,S(x))
+ res(x). On each subinterval
of the mesh, a norm of the residual in the i
th
component of the solution, res(i)
, is estimated
and is required to be less than or equal to a tolerance. This tolerance
is a function of the relative and absolute tolerances, RelTol
and AbsTol
,
defined by the user.
$$\parallel \left(\text{res}(i)/\mathrm{max}\left(\text{abs}\left(f(i)\right),\text{AbsTol}(i)/\text{RelTol}\right)\right)\parallel \text{\hspace{0.17em}}\le \text{RelTol}$$
The following table describes the error tolerance properties.
BVP Error Tolerance Properties
Vectorization
The following table describes the BVP vectorization property.
Vectorization of the ODE function used by bvp4c
differs
from the vectorization used by the ODE solvers:
For
bvp4c
, the ODE function must be vectorized with respect to the first argument as well as the second one, so thatF([x1 x2 ...],[y1 y2 ...])
returns[F(x1,y1) F(x2,y2)...]
.bvp4c
benefits from vectorization even when analytical Jacobians are provided. For stiff ODE solvers, vectorization is ignored when analytical Jacobians are used.
Vectorization Properties
Property  Value  Description 


 Set on to inform With the MATLAB^{®} array notation, it is typically an easy matter to vectorize an ODE
function. In the function dydx = shockODE(x,y,e) pix = pi*x; dydx = [ y(2,:)... x/e.*y(2,:)pi^2*cos(pix) pix/e.*sin(pix)]; 
Analytical Partial Derivatives
By default, the bvp4c
solver
approximates all partial derivatives with finite differences. bvp4c
can
be more efficient if you provide analytical partial derivatives ∂f/∂y of
the differential equations, and analytical partial derivatives, ∂bc/∂ya and
∂bc/∂yb, of the
boundary conditions. If the problem involves unknown parameters, you
must also provide partial derivatives, ∂f/∂p and
∂bc/∂p, with respect
to the parameters.
The following table describes the analytical partial derivatives properties.
BVP Analytical Partial Derivative Properties
Property  Value  Description 

 Function handle  A function handle that computes the analytical partial
derivatives of f(x,y).
When solving y′ = f(x,y),
set this property to 
 Function handle  A function handle that computes the analytical partial
derivatives of bc(ya,yb).
For boundary conditions bc(ya,yb),
set this property to 
Singular BVPs
bvp4c
can solve singular problems of the
form
$${y}^{\prime}=S\frac{y}{x}+f(x,y,p)$$
posed on the interval [0,b] where b >
0. For such problems, specify the constant matrix S as
the value of SingularTerm
. For equations of this
form, odefun
evaluates only the f(x,y,p)
term, where p represents unknown parameters, if
any.
Singular BVP Property
Property  Value  Description 

 Constant matrix  Singular term of singular BVPs. Set to the constant matrix S for equations of the form $${y}^{\prime}=S\frac{y}{x}+f(x,y,p)$$ posed on the interval [0,b] where b > 0. 
Mesh Size Property
bvp4c
solves a system
of algebraic equations to determine the numerical solution to a BVP
at each of the mesh points. The size of the algebraic system depends
on the number of differential equations (n
) and
the number of mesh points in the current mesh (N
).
When the allowed number of mesh points is exhausted, the computation
stops, bvp4c
displays a warning message and returns
the solution it found so far. This solution does not satisfy the error
tolerance, but it may provide an excellent initial guess for computations
restarted with relaxed error tolerances or an increased value of NMax
.
The following table describes the mesh size property.
BVP Mesh Size Property
Property  Value  Description 

 positive integer {  Maximum number of mesh points allowed when solving the
BVP, where 
Solution Statistic Property
The Stats
property lets you view solution
statistics.
The following table describes the solution statistics property.
BVP Solution Statistic Property
Property  Value  Description 


 Specifies whether statistics about the computations are
displayed. If the

Examples
To create an options structure that changes the relative error
tolerance of bvp4c
from the
default value of 1e3
to 1e4
,
enter
options = bvpset('RelTol',1e4);
To recover the value of 'RelTol'
from options
,
enter
bvpget(options,'RelTol') ans = 1.0000e004
Version History
Introduced before R2006a