`bvp5c`

Solves boundary value problems with a fourth-order method that controls the true error.

Category: Mathematics > Numerical Integration and Differential Equations

Syntax

sol = bvp5c(odefun, bcfun, solinit)

Solves the system y' = odefun(x, y) with boundary conditions bcfun(y(a), y(b)) = 0.

sol = bvp5c(odefun, bcfun, solinit, options)

Also applies options from bvpset.

Description

bvp5c has the same calling pattern as bvp4c, so one can often be swapped for the other. The difference is in the error control: bvp4c limits the residual of the collocation polynomial, while bvp5c limits the error in the solution itself, which can matter when a tight tolerance is required.

If one solver stalls on a hard problem, try the other, and improve the initial guess.

Input arguments

odefun, bcfun: Function handles for the equations and for the boundary residuals, as for bvp4c.
solinit: Initial mesh and guess from bvpinit.
options: Structure from bvpset.

Output arguments

sol: Structure with the fields x, y, yp and stats, usable with deval.

Example

Same problem as bvp4c

odefun = @(x, y) [y(2); -y(1)];
bcfun = @(ya, yb) [ya(1); yb(1) - 1];
solinit = bvpinit(linspace(0, 1, 5), [0; 1]);
sol = bvp5c(odefun, bcfun, solinit);
y = deval(sol, 0.5);
fprintf('%.4f\n', y(1))

Output

0.5697

bvp5c