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An error estimate for Volterra integral equations
Springer Science and Business Media LLC - - 1971
G. M. Phillips
A generalization of singly-implicit methods
Springer Science and Business Media LLC - Tập 21 - Trang 175-189 - 1981
J. C. Butcher
Singly-implicit Runge-Kutta methods are characterized by a one-point spectrum property of the coefficient matrix. If a method of this type is also a collocation method, then its abscissae are proportional to the zeros of a Laguerre polynomial. The generalization introduced here is a multistep method in the style of Nordsieck and also a multistage method under the one-point spectrum constraint. It ... hiện toàn bộ
Convex interval interpolation with cubic splines, II
Springer Science and Business Media LLC - Tập 31 - Trang 328-340 - 1991
Jochen W. Schmidt
The problem of convex interval interpolation with cubicC 1-splines has an infinite number of solutions, if it is solvable at all. For selecting one of the solutions a regularized mean curvature is minimized. The arising finite dimensional constrained program is solved numerically by means of a dualization approach.
An application of Chawla's identity to a different scheme for singular problems
Springer Science and Business Media LLC - Tập 30 - Trang 566-568 - 1990
Manabu Sakai, Riaz A. Usmani
Computation of connection coefficients and measure modifications for orthogonal polynomials
Springer Science and Business Media LLC - Tập 52 - Trang 457-483 - 2011
Akil Narayan, Jan S. Hesthaven
We observe that polynomial measure modifications for families of univariate orthogonal polynomials imply sparse connection coefficient relations. We therefore propose connecting L 2 expansion coefficients between a polynomial family and a modified family by a sparse transformation. Accuracy and conditioning of the connection and its inverse are explored. The connection and recurrence coefficients ... hiện toàn bộ
Non-uniform interpolatory curve subdivision with edge parameters built upon compactly supported fundamental splines
Springer Science and Business Media LLC - Tập 51 - Trang 781-808 - 2011
Carolina Vittoria Beccari, Giulio Casciola, Lucia Romani
In this paper we present a family of Non-Uniform Local Interpolatory (NULI) subdivision schemes, derived from compactly supported interpolatory fundamental splines with non-uniform knots (NULIFS). For this spline family, the knot-partition is defined by a sequence of break points and by one additional knot, arbitrarily placed along each knot-interval. The resulting refinement algorithms are linear... hiện toàn bộ
Numerical integration based on bivariate quadratic spline quasi-interpolants on Powell-Sabin partitions
Springer Science and Business Media LLC - Tập 53 - Trang 175-192 - 2012
P. Sablonnière, D. Sbibih, M. Tahrichi
In this paper we generate and study new cubature formulas based on spline quasi-interpolants in the space of quadratic Powell-Sabin splines on nonuniform triangulations of a polygonal domain in ℝ2. By using a specific refinement of a generic triangulation, optimal convergence orders are obtained for some of these rules. Numerical tests are presented for illustrating the theoretical results.
Two new approaches for solving elliptic obstacle problems using discontinuous Galerkin methods
Springer Science and Business Media LLC - Tập 62 - Trang 89-124 - 2021
Sharat Gaddam, Thirupathi Gudi, Kamana Porwal
The main aim of this article is to present two new ways to solve the elliptic obstacle problem by using discontinuous Galerkin finite element methods. In Gaddam and Gudi (Comput Methods Appl Math 18:223–236, 2018. https://doi.org/10.1515/cmam-2017-0018 ), a bubble enriched conforming quadratic finite element method is introduced and analyzed for the obstacle problem in dimension 3. In this article... hiện toàn bộ
Các ứng dụng của thiết bị lưu trữ băng từ, facit ECM64 (Bộ nhớ Carousel) Dịch bởi AI
Springer Science and Business Media LLC - Tập 2 - Trang 16-20 - 1962
Olle Karlqvist
Thiết bị lưu trữ băng từ, ECM 64 hay còn gọi là “Bộ nhớ Carousel”, đã được phát triển bởi Facit Electronics AB, Stockholm. Nguyên mẫu của Bộ nhớ đã được kết nối với máy tính Facit EDB 3 trong một năm rưỡi. Các ứng dụng liên quan đến Bộ nhớ Carousel được đề cập ở đây xuất phát từ việc sử dụng máy tính này bởi Cục Dịch vụ Facit tại Stockholm. Mặc dù là một nguyên mẫu nhưng Bộ nhớ Carousel hoạt động ... hiện toàn bộ
Fourier analysis of schwarz alternating methods for piecewise hermite bicubic orthogonal spline collocation
Springer Science and Business Media LLC - Tập 33 - Trang 634-646 - 1993
Bernard Bialecki, D. Scott Dillery
The rates of convergence of two Schwarz alternating methods are analyzed for the iterative solution of a discrete problem which arises when orthogonal spline collocation with piecewise Hermite bicubics is applied to the Dirichlet problem for Poisson's equation on a rectangle. In the first method, the rectangle is divided into two overlapping subrectangles, while three overlapping subrectangles are... hiện toàn bộ
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