A challenging test for convergence accelerators: summation of a series with a special sign pattern.
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Displaying 1 – 20 of 174
A comparison of three high-precision quadrature schemes.
Bailey, David H., Jeyabalan, Karthik, Li, Xiaoye S. (2005)
Experimental Mathematics
A Contour Integral Representation of Linear Extrapolation Methods.
Guido Walz (1987)
Numerische Mathematik
A Derivative-Free Transformation Preserving the Order of Convergence of Iteration Methods in Case of Multiple Zeros.
J.B. Kioustelidis (1979)
Numerische Mathematik
A direct global superconvergence analysis for Sobolev and viscoelasticity type equations
Qun Lin, Shu Hua Zhang (1997)
Applications of Mathematics
In this paper we study the finite element approximations to the Sobolev and viscoelasticity type equations and present a direct analysis for global superconvergence for these problems, without using Ritz projection or its modified forms.
A full multigrid method for semilinear elliptic equation
Fei Xu, Hehu Xie (2017)
Applications of Mathematics
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as...
A General Extrapolation Algorithm.
C. Brezinski (1980)
Numerische Mathematik
A general inequality of Grüss type.
Ren, Hongmin, Yang, Shijun (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
A matrix analysis of the stability of the Clenshaw algorithm.
Roberto Barrio (1998)
Extracta Mathematicae
A Method of Characteristics Solving the Initial-Boundary Value Problem of a Hyperbolic Differential Equation of Second Order.
W. Hackbusch, S. Dittrich (1980)
Numerische Mathematik
A multilevel Newton's method for eigenvalue problems
Yunhui He, Yu Li, Hehu Xie, Chun'guang You, Ning Zhang (2018)
Applications of Mathematics
We propose a new type of multilevel method for solving eigenvalue problems based on Newton's method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue...
A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction
Roland Ernst, Bernd Flemisch, Barbara Wohlmuth (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.
A new mixed finite element method based on the Crank-Nicolson scheme for Burgers' equation
Xiaohui Hu, Pengzhan Huang, Xinlong Feng (2016)
Applications of Mathematics
In this paper, a new mixed finite element method is used to approximate the solution as well as the flux of the 2D Burgers’ equation. Based on this new formulation, we give the corresponding stable conforming finite element approximation for the pair by using the Crank-Nicolson time-discretization scheme. Optimal error estimates are obtained. Finally, numerical experiments show the efficiency of the new mixed method and justify the theoretical results.
A New Technique for Rational Extrapolation to the Limit.
L. WUYTACK (1971)
Numerische Mathematik
A note on matrix summability and rates on convergence
H. I. Miller (1973)
Matematički Vesnik
A priori Estimates for Truncation Error of Continued Fractions K(1 bn)
D.A. Field, W.B. Jones (1972)
Numerische Mathematik
A simple recursive estimator with on-line orthogonalization of the input sequence
Jaroslav Markl (1983)
Kybernetika
A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation
O. Awono, J. Tagoudjeu (2010)
Mathematical Modelling of Natural Phenomena
We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...
A Superconvergence result for mixed finite element approximations of the eigenvalue problem
Qun Lin, Hehu Xie (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic...
A Superconvergence result for mixed finite element approximations of the eigenvalue problem∗
Qun Lin, Hehu Xie (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
In this paper, we present a superconvergence result for the mixed finite element approximations of general second order elliptic eigenvalue problems. It is known that a superconvergence result has been given by Durán et al. [Math. Models Methods Appl. Sci. 9 (1999) 1165–1178] and Gardini [ESAIM: M2AN 43 (2009) 853–865] for the lowest order Raviart-Thomas approximation of Laplace eigenvalue problems. In this work, we introduce a new way to derive the superconvergence of general second order elliptic...
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