"bvp4c is a finite difference code that implements the three-stage Lobatto IIIa formula. This is a collocation formula and the collocation polynomial provides a C1-continuous solution that is fourth-order accurate uniformly in [a,b]. Mesh selection and error control are based on the residual of the continuous solution."
and it gives a reference there to http://www.mathworks.com/matlabcentral/fileexchange/3819-tutorial-on-solving-bvps-with-bvp4c which appears to have been written by the author of the code.
