A O(h) cubic spline collocation method for quasilinear parabolic equation

A modified version of the usual cubic spline collocation method is proposed and analyzed for quasilinear parabolic problems. Continuous time estimates of order O(h) are obtained, via arguments based on certain discrete inner-products for a uniform mesh and sufficiently smooth problems. Two types of collocation at the boundary are studied and shown to yield O(h) and O(h^(7/2)) rates of convergence.