Error analysis for spline collocation methods with application to knot selection
HTML articles powered by AMS MathViewer
- by J. Christiansen and R. D. Russell PDF
- Math. Comp. 32 (1978), 415-419 Request permission
Abstract:
Some collocation schemes used to solve mth order ordinary differential equations are known to display superconvergence at the mesh points. Here we show that some such schemes have additional superconvergence points for the approximate solution and all of its derivatives. Using such points, we argue that a mesh selection scheme introduced by Dodson can be expected to perform well under general circumstances. A numerical example is given to demonstrate the new superconvergence results.References
- Carl de Boor, Good approximation by splines with variable knots. II, Conference on the Numerical Solution of Differential Equations (Univ. Dundee, Dundee, 1973) Lecture Notes in Math., Vol. 363, Springer, Berlin, 1974, pp. 12–20. MR 0431606
- Carl de Boor and Blâir Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973), 582–606. MR 373328, DOI 10.1137/0710052 D. J. DODSON, Optimal Order Approximation by Spline Functions, Ph.D. Thesis, Purdue Univ., 1972.
- R. D. Russell and J. Christiansen, Adaptive mesh selection strategies for solving boundary value problems, SIAM J. Numer. Anal. 15 (1978), no. 1, 59–80. MR 471336, DOI 10.1137/0715004 A. B. WHITE, JR., On Selection of Equidistributing Meshes for Two-Point Boundary-Value Problems, Report 112, Univ. of Texas, Center Numer. Anal., 1976.
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 415-419
- MSC: Primary 65L10
- DOI: https://doi.org/10.1090/S0025-5718-1978-0494963-2
- MathSciNet review: 0494963