Das, Pratibhamoy
Published in
Numerical Algorithms

The present work considers a nonlinear system of singularly perturbed delay differential equation whose each component of the solution has multiple layers. Here, we provide an a posteriori based convergence analysis for the adaptation of these layer phenomena. We derive a parameter uniform a posteriori error estimate which will lead to a layer adap...

Bu, Weiping Xiao, Aiguo
Published in
Numerical Algorithms

In this paper, we develop an h-p version of finite element method for one-dimensional fractional differential equation −0Dxαu+Au=f(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begi...

Zhang, Yunong Qi, Zhiyuan Li, Jian Qiu, Binbin Yang, Min
Published in
Numerical Algorithms

Future optimization, which is also known as discrete-time time-variant optimization problem, is an important issue in scientific fields. Recently, Guo et al. have proposed a new effective three-step discrete-time zeroing dynamics (DTZD) model (Guo et al. Numer. Algorithms 77(1), 23–36, 2018) to solve future optimization problems, which is discretiz...

Cao, Mingyuan Huang, Qingdao Yang, Yueting
Published in
Numerical Algorithms

A self-adaptive trust region method is presented for finding the largest or smallest ℬ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {B}$\end{document}-eigenva...

Zhao, M. Wu, H. Xiong, C.
Published in
Numerical Algorithms

In this article, we study the HDG approximation for the obstacle problem, i.e., variational inequalities, with remarkable convergence properties. Using polynomials of degree k ≥ 0 for both the potential u and the flux q, we show that the approximations of the potential and flux converge in L2 with the optimal order of k + 1 . The approximate trace ...

Huang, Na Ma, Chang-Feng
Published in
Numerical Algorithms

In this work, we consider some preconditioning techniques for a class of 3 × 3 block saddle point problems, which arise from finite element methods for solving time-dependent Maxwell equations and some other applications. We propose an exact block diagonal preconditioner for solving the symmetric saddle point problem and its nonsymmetric form. We s...

Huang, Baohua Ma, Changfeng
Published in
Numerical Algorithms

The present work proposes a finite iterative algorithm to find the least squares solutions of periodic matrix equations over symmetric ξ-periodic matrices. By this algorithm, for any initial symmetric ξ-periodic matrices, the solution group can be obtained in finite iterative steps in the absence of round-off errors, and the solution group with lea...

Jo, Gwanghyun Kwak, Do Y.
Published in
Numerical Algorithms

In this work, we develop geometric multigrid algorithms for the immersed finite element methods for elliptic problems with interface (Chou et al. Adv. Comput. Math. 33, 149–168 2010; Kwak and Lee, Int. J. Pure Appl. Math. 104, 471–494 2015; Li et al. Numer. Math. 96, 61–98 2003, 2004; Lin et al. SIAM J. Numer. Anal. 53, 1121–1144 2015). We need to ...

Anderson, Donald G. M.
Published in
Numerical Algorithms

The Extrapolation Algorithm is a technique devised in 1962 for accelerating the rate of convergence of slowly converging Picard iterations for fixed point problems. Versions to this technique are now called Anderson Acceleration in the applied mathematics community and Anderson Mixing in the physics and chemistry communities, and these are related ...

Brugnano, Luigi Montijano, Juan I. Rández, Luis
Published in
Numerical Algorithms

Multi-frequency, highly oscillatory Hamiltonian problems derive from the mathematical modelling of many real-life applications. We here propose a variant of Hamiltonian Boundary Value Methods (HBVMs), which is able to efficiently deal with the numerical solution of such problems. We present algorithms to select the parameters of the methods that al...