Ludzie pragną czasami się rozstawać, żeby móc tęsknić, czekać i cieszyć się z powrotem.
x is a vector that specifies an initial mesh. If you want to solve the boundary
value problem (BVP) on [ a, b] , then specify x(1) as a and x(end) as b . The function bvp4c adapts this mesh to the solution, so often a guess like
x = linspace(a,b,10) suffices. However, in difficult cases, you must place
mesh points where the solution changes rapidly. The entries of x must be
ordered and distinct, so if a < b , then x(1) < x(2) < ... < x(end), and similarly for a > b .
v is a guess for the solution. It can be either a vector, or a function:
• Vector – For each component of the solution, bvpinit replicates the
corresponding element of the vector as a constant guess across all mesh
points. That is, v(i) is a constant guess for the ith component y(i,:) of the
solution at all the mesh points in x.
• Function – For a given mesh point, the function must return a vector whose elements are guesses for the corresponding components of the solution. The
function must be of the form
y = guess(x)
where x is a mesh point and y is a vector whose length is the same as the
number of components in the solution. For example, if you use @guess,
bvpinit calls this function for each mesh point y(:,j) = guess(x(j)).
solinit = bvpinit(x,v,parameters) indicates that the BVP involves
unknown parameters. Use the vector parameters to provide a guess for all
unknown parameters.
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bvpinit
solinit is a structure with the following fields. The structure can have any
name, but the fields must be named x, y, and parameters.
x
Ordered nodes of the initial mesh.
y
Initial guess for the solution with solinit.y(:,i) a guess for
the solution at the node solinit.x(i).
parameters
Optional. A vector that provides an initial guess for unknown
parameters.
solinit = bvpinit(sol,[anew bnew]) forms an initial guess on the interval
[anew bnew] from a solution sol on an interval [ a, b] . The new interval must be larger than the previous one, so either anew <= a < b <= bnew or anew >= a > b >= bnew. The solution sol is extrapolated to the new interval.
If sol contains parameters, they are copied to solinit.
solinit = bvpinit(sol,[anew bnew],parameters) forms solinit as
described above, but uses parameters as a guess for unknown parameters in
solinit.
See Also
@ (function_handle), bvp4c, bvpget, bvpset, deval
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bvpset
2bvpset
Purpose
Create/alter boundary value problem (BVP) options structure
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 in which the named properties have the specified values.
Any unspecified properties have default values. It is sufficient to type only the
leading characters that uniquely identify the property. Case is ignored for
property names.
options = bvpset(oldopts,'name1',value1,...) alters an existing options
structure oldopts.
options = bvpset(oldopts,newopts) combines an existing options structure
oldopts with a new options structure newopts. Any new properties overwrite
corresponding old properties.
bvpset with no input arguments displays all property names and their possible
values.
BVP Properties
These properties are available.
Property
Value
Description
RelTol
Positive scalar
A relative tolerance that applies to all components of the
{1e-3}
residual vector. The computed solution S( x) is the exact
solution of S′( x) = F( x, S( x)) + res( x). On each subinterval of the mesh, the residual res( x) satisfies
(res(i)/max(abs(F(i)),AbsTol(i)/RelTol)) ≤ RelTol
AbsTol
Positive scalar or
An absolue tolerance that applies to all components of the
vector {1e-6}
residual vector. Elements of a vector of tolerances apply to
corresponding components of the residual vector.
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bvpset
Property
Value
Description
Vectorized
on | {off}
Set on to inform bvp4c that you have coded the ODE
function F so that F([x1 x2 ...],[y1 y2 ...]) returns
[F(x1,y1) F(x2,y2) ...]. That is, your ODE function can