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Form the initial guess for bvp4c



solinit = bvpinit(x,yinit) forms the initial guess for the boundary value problem solver bvp4c.

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 a guess like x = linspace(a,b,10) often suffices. However, in difficult cases, you should place mesh points where the solution changes rapidly. The entries of x must be in

For two-point boundary value problems, the entries of x must be distinct. That is, if , the entries must satisfy x(1) < x(2) < ... < x(end). If , the entries must satisfy x(1) > x(2) > ... > x(end)

For multipoint boundary value problem, you can specify the points in at which the boundary conditions apply, other than the endpoints a and b, by repeating their entries in x. For example, if you set

the boundary conditions apply at three points: the endpoints 0 and 2, and the repeated entry 1. In general, repeated entries represent boundary points between regions in . In the preceding example, the repeated entry 1 divides the interval [0,2] into two regions: [0,1] and [1,2].

yinit is a guess for the solution. It can be either a vector, or a function:

solinit = bvpinit(x,yinit,parameters) indicates that the boundary value problem 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 x, y, and parameters.

Ordered nodes of the initial mesh.
Initial guess for the solution with solinit.y(:,i) a guess for the solution at the node solinit.x(i).
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 . 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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