# bvpxtend

Form guess structure for extending boundary value solutions

## Syntax

```solinit = bvpxtend(sol,xnew,ynew) solinit = bvpxtend(sol,xnew,extrap) solinit = bvpxtend(sol,xnew) solinit = bvpxtend(sol,xnew,ynew,pnew) solinit = bvpxtend(sol,xnew,extrap,pnew) ```

## Description

`solinit = bvpxtend(sol,xnew,ynew)` uses solution `sol` computed on `[a,b]` to form a solution guess for the interval extended to `xnew`. The extension point `xnew` must be outside the interval `[a,b]`, but on either side. The vector `ynew` provides an initial guess for the solution at `xnew`.

`solinit = bvpxtend(sol,xnew,extrap)` forms the guess at `xnew` by extrapolating the solution `sol`. `extrap` has three possible values:

• `'constant'``ynew` is a value nearer to end point of solution in `sol`.

• `'linear'``ynew` is a value at `xnew` of linear interpolant to the value and slope at the nearer end point of solution in `sol`.

• `'solution'``ynew` is the value of (cubic) solution in `sol` at `xnew`.

The value of `extrap` also can be a string.

`solinit = bvpxtend(sol,xnew)` uses the extrapolating solution where `extrap` is `'constant'`. If there are unknown parameters, values present in `sol` are used as the initial guess for parameters in `solinit`.

`solinit = bvpxtend(sol,xnew,ynew,pnew)` specifies a different guess `pnew`. `pnew` can be used with extrapolation, using the syntax ```solinit = bvpxtend(sol,xnew,extrap,pnew)```. To modify parameters without changing the interval, use `[]` as place holder for `xnew` and `ynew`.