TABLE OF CONTENTS The function bvp4c uses a collocation method to solve systems of ODEs in two-point boundary value form. These systems may be written
Here, as for the initial value problem in the previous section, y(x) is an unknown m-vector and f is a given function of x and y that also produces an m-vector. The solution is required over the range a ? x ? b and the given function g specifies the boundary conditions. Note that the independent variable was labeled t in the previous section and is now labeled x. This is consistent with MATLAB's documentation and reflects the fact that two-point boundary value problems (BVPs) usually arise over an interval of space rather than time. Generally, BVPs are more computationally challenging than initial value problems. In particular, it is common for more than one solution to exist. For this reason, bvp4c requires an initial guess to be supplied for the solution. The initial guess and the final solution are stored in structures (see Section 18.3). We introduce bvp4c through a simple example before giving more details.
A scalar BVP describing the cross-sectional shape of a water droplet on a flat surface is given by [66]
Here, h(x) measures the height of the droplet at point x. We set y1( x) = h(x) and y2(x) = dh(x)/dx and rewrite the equation as a system of...
