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Least squares methods for solving differential equations using Bézier control points. (English) Zbl 1048.65077
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.
MSC:
65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B15Nonlinear boundary value problems for ODE
65L20Stability and convergence of numerical methods for ODE