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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
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References:
[1] Aktas, Z.; Stetter, J. H.: A classification and survey of numerical methods for boundary value problems in ordinary differential equations. Internat. J. Numer. meth. Engrg. 11, 771-796 (1977) · Zbl 0359.65070
[2] Ascher, U.: Discrete least squares approximations for ordinary differential equations. SIAM J. Numer. anal. 15, 478-496 (1978) · Zbl 0414.65049
[3] Ciarlet, P. G.: Finite element methods for elliptic problems. (1978) · Zbl 0383.65058
[4] De Boor, C.: A practical guide to splines. (1978) · Zbl 0406.41003
[5] Farin, G.: Curves and surfaces for computer aided geometric design, A practical guide. (1997) · Zbl 0919.68120
[6] Jiang, B. N.: On least squares method. Comput. meth. Appl. mech. Engrg. 152, 239-257 (1998) · Zbl 0968.76040
[7] Johnson, R. W.; Landon, M. B.: A B-spline collocation method to approximate the solutions to the equations of fluid dynamics. Proceedings of the 3rd ASME/JSME joint fluid engineering conference (1999)
[8] Keller, H. B.: Numerical methods for two-point boundary-value problems. (1968) · Zbl 0172.19503
[9] Lai, M. J.; Wenston, P.: Bivariate spline method for numerical solution of Navier--Stokes equations over polygons in stream function formulation. Numer. methods PDE 16, 147-183 (2000) · Zbl 0968.76041
[10] Nairn, D.; Peters, J.; Lutterkort, D.: Sharp, quantitative bounds on the distance between a polynomial piece and its Bézier control polygon. Comput. aided geometric design 16, 613-631 (1999) · Zbl 0997.65016
[11] Prautzsch, H.; Kobbelt, L.: Convergence of subdivision and degree elevation. Adv. comput. Math. 2, 143-154 (1994) · Zbl 0829.65012
[12] Quarteroni, A.; Sacco, R.; Saleri, F.: Numerical mathematics. (2000) · Zbl 0957.65001
[13] Shariff, K.; Moser, R. D.: Two-dimensional mesh embedding for B-spline methods. J. comput. Phys. 145, 471-488 (1998) · Zbl 0910.65083