Least squares methods for solving differential equations using Bézier control points

Applied Numerical Mathematics

Volumn 48, Issue 2, 2004, Pages 237-252

  Zheng, Jianmin ^a   Sederberg, Thomas W ^a   Johnson, Richard W ^b  

^a 3361 TMCB   (United States)

^b IDAHO NATIONAL LABORATORY   (United States)

Author keywords

B zier control points; Boundary value problem; Degree raising; Differential equations; Least squares method; Subdivision

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL METHODS; COMPUTER AIDED DESIGN; FINITE ELEMENT METHOD; FUNCTIONS; LAGRANGE MULTIPLIERS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; PROBLEM SOLVING;

CONTROL POINTS; DEGREE RAISING; RESIDUAL FUNCTION;

LEAST SQUARES APPROXIMATIONS;

EID: 0348046421     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2002.01.001     Document Type: Article

References (13)

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. 11:1977;771-796.
2. Ascher U. Discrete least squares approximations for ordinary differential equations. SIAM J. Numer. Anal. 15:1978;478-496.
3. Ciarlet P.G. Finite Element Methods for Elliptic Problems. 1978;North-Holland, New York.
4. de Boor C. A Practical Guide to Splines. 1978;Springer, New York.
5. Farin G. Curves and Surfaces for Computer Aided Geometric Design, A Practical Guide. 4th Edition: 1997;Academic Press, New York.
6. Jiang B.N. On least squares method. Comput. Meth. Appl. Mech. Engrg. 152:1998;239-257.
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. July 18-23, San Francisco, Forum F-217: 1999.
8. Keller H.B. Numerical Methods for Two-Point Boundary-Value Problems. 1968;Blaisdell, Waltham, MA. MR 37#6038.
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. 16:2000;147-183.
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. 16:1999;613-631.
11. Prautzsch H., Kobbelt L. Convergence of subdivision and degree elevation. Adv. Comput. Math. 2:1994;143-154.
12. Quarteroni A., Sacco R., Saleri F. Numerical Mathematics. 2000;Springer, Berlin.
13. Shariff K., Moser R.D. Two-dimensional mesh embedding for B-spline methods. J. Comput. Phys. 145:1998;471-488.