Error analysis for spline collocation methods with application to knot selection
نویسندگان
چکیده
منابع مشابه
Error Analysis for Spline Collocation Methods With Application to Knot Selection
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 c...
متن کاملApplication of linear combination between cubic B-spline collocation methods with different basis for solving the KdV equation
In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using a new approach by combining cubic B-spline functions. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms L2, L∞ are computed. Three invariants of motion are...
متن کاملSPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS
The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...
متن کاملQuadratic spline quasi-interpolants and collocation methods
Univariate and multivariate quadratic spline quasi-interpolants provide interesting approximation formulas for derivatives of approximated functions that can be very accurate at some points thanks to the superconvergence properties of these operators. Moreover, they also give rise to good global approximations of derivatives on the whole domain of definition. From these results, some collocatio...
متن کاملMeshless Collocation: Error Estimates with Application to Dynamical Systems
In this paper, we derive error estimates for generalized interpolation, in particular collocation, in Sobolev spaces. We employ our estimates to collocation problems using radial basis functions and extend and improve previously known results for elliptic problems. Finally, we use meshless collocation to approximate Lyapunov functions for dynamical systems.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1978
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1978-0494963-2