Least squares methods for solving differential equations using Bézier control points. (Q1427213)

The authors consider the least squares approach to solve boundary value problems of ordinary differential equations, with the particularity that instead of computing integrals or performing discretization, a least squares objective function is establish based on the Bezier control points. Two least squares type schemes based on degree raising and subdivision are proposed. These schemes are further analyzed from the convergence point of view in the case of two-point boundary value problems.