`bvpxtend`

Extends a boundary value problem solution to a new interval end.

Category: Mathematics > Numerical Integration and Differential Equations

Syntax

solext = bvpxtend(sol, xnew, ynew)

Returns a guess on the interval extended to xnew, starting from sol and the value ynew at the new point.

Description

This is the basis of continuation: solve an easy problem on a short interval, extend the guess, and solve again on a longer one, repeating until the target interval is reached. It helps with problems that are hard to start from a crude guess.

The extension is only a guess; you must still call the solver with the new boundary conditions.

Input arguments

sol: Solution structure from bvp4c or bvp5c.
xnew: New end point, outside the current interval.
ynew: Guess for the solution at xnew (optional).

Output arguments

solext: Structure usable as the solinit argument of a new solver call on the longer interval.

Example

Extending the interval

odefun = @(x, y) [y(2); -y(1)];
bcfun = @(ya, yb) [ya(1); yb(1) - 1];
sol = bvp4c(odefun, bcfun, bvpinit(linspace(0, 1, 5), [0; 1]));
solext = bvpxtend(sol, 2, [1; 0]);
solext.x(end)

Output

ans = 2

bvpxtend