|MATLAB Function Reference|
Form the initial guess for
solinit = bvpinit(x,v)
forms the initial guess for
bvp4c in common circumstances.
x is a vector that specifies an initial mesh. If you want to solve the boundary value problem (BVP) on , then specify
x(1) as and
x(end) as . 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 , then
x(1) < x(2) < ... < x(end), and similarly for .
v is a guess for the solution. It can be either a vector, or a function:
bvpinitreplicates the corresponding element of the vector as a constant guess across all mesh points. That is,
v(i)is a constant guess for the
y(i,:)of the solution at all the mesh points in
xis a mesh point and
yis a vector whose length is the same as the number of components in the solution. For example, if you use
bvpinitcalls 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.
solinit is a structure with the following fields. The structure can have any name, but the fields must be named
||Ordered nodes of the initial mesh.
||Initial guess for the solution with
solinit = bvpinit(sol,[anew bnew])
forms an initial guess on the interval
[anew bnew] from a solution
sol on an interval . The new interval must be larger than the previous one, so either
anew <= a
<= bnew or
anew >= a
>= bnew. The solution
sol is extrapolated to the new interval. If
parameters, they are copied to
solinit = bvpinit(sol,[anew bnew],parameters)
solinit as described above, but uses
parameters as a guess for unknown parameters in