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We study a posteriori error analysis of linear-quadratic boundary control problems under bilateral box constraints on the control which acts through a Neumann type boundary condition. We adopt the hybridizable discontinuous Galerkin method…

Numerical Analysis · Mathematics 2020-04-21 Haitao Leng , Yanping Chen

Using an original method, we find the algebra of generalized symmetries of a remarkable (1+2)-dimensional ultraparabolic Fokker-Planck equation, which is also called the Kolmogorov equation and is singled out within the entire class of…

Mathematical Physics · Physics 2025-09-01 Dmytro R. Popovych , Serhii D. Koval , Roman O. Popovych

Fractional calculus with respect to function $\psi$, also named as $\psi$-fractional calculus, generalizes the Hadamard and the Riemann-Liouville fractional calculi, which causes challenge in numerical treatment. In this paper we study…

Numerical Analysis · Mathematics 2023-12-29 Tinggang Zhao , Zhenyu Zhao , Changpin Li , Dongxia Li

A numerical method is proposed to compute a low-rank Galerkin approximation to the solution of a parametric or stochastic equation in a non-intrusive fashion. The considered nonlinear problems are associated with the minimization of a…

Numerical Analysis · Mathematics 2017-05-11 Loïc Giraldi , Dishi Liu , Hermann G. Matthies , Anthony Nouy

We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…

Fluid Dynamics · Physics 2018-03-14 Ravindra Pethiyagoda , Timothy J. Moroney , Scott W. McCue

This paper concerns the well-posedness and uniform stabilization of the Petrovsky-Wave Nonlinear coupled system with strong damping. Existence of global weak solutions for this problem is established by using the Galerkin method. Meanwhile,…

Analysis of PDEs · Mathematics 2021-03-11 Akram Ben Aissa

This paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing…

Quantum Physics · Physics 2023-07-25 Yulong Dong , Lin Lin , Hongkang Ni , Jiasu Wang

We propose new iterative methods for computing nontrivial extremal generalized singular values and vectors. The first method is a generalized Davidson-type algorithm and the second method employs a multidirectional subspace expansion…

Numerical Analysis · Mathematics 2017-05-18 Ian N. Zwaan , Michiel E. Hochstenbach

We develop a unified Petrov-Galerkin spectral method for a class of fractional partial differential equations with two-sided derivatives and constant coefficients of the form $ _{0}{\mathcal{D}}_{t}^{2\tau}u^{} + \sum_{i=1}^{d}$ $[c_{l_i}$…

Computational Engineering, Finance, and Science · Computer Science 2019-10-02 M. Samiee , M. Zayernouri. Mark M. Meerschaert

Our problem is to accurately solve linear systems on a general purpose graphics processing unit with double double and quad double arithmetic. The linear systems originate from the application of Newton's method on polynomial systems.…

Mathematical Software · Computer Science 2013-01-15 Jan Verschelde , Genady Yoffe

The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…

Dynamical Systems · Mathematics 2016-03-04 Laura Menini , Corrado Possieri , Antonio Tornambè

We analyse a class of nonoverlapping domain decomposition preconditioners for nonsymmetric linear systems arising from discontinuous Galerkin finite element approximation of fully nonlinear Hamilton--Jacobi--Bellman (HJB) partial…

Numerical Analysis · Mathematics 2024-12-06 Iain Smears

We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations…

Numerical Analysis · Mathematics 2023-05-18 Giuseppe Orlando

We prove a set of general theorems that provide new nonlocal constants and first integrals for nonlinear Jacobi-type ordinary differential equations. Applications include equations of the Painleve-Gambier classification.

Classical Analysis and ODEs · Mathematics 2022-03-30 Mattia Scomparin

This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first…

Numerical Analysis · Mathematics 2024-02-05 Matteo Losacco , Alberto Fossà , Roberto Armellin

We describe two main classes of one-sided trigonometric and hyperbolic Jacobi-type algorithms for computing eigenvalues and eigenvectors of Hermitian matrices. These types of algorithms exhibit significant advantages over many other…

Numerical Analysis · Computer Science 2020-03-18 Sanja Singer , Sasa Singer , Vedran Novakovic , Aleksandar Uscumlic , Vedran Dunjko

Geometry of sparse systems of polynomial equations (i.e. the ones with prescribed monomials and generic coefficients) is well studied in terms of their Newton polytopes. The results of this study are colloquially known as the…

Algebraic Geometry · Mathematics 2024-01-23 Alexander Esterov

This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochastic Galerkin method.…

Numerical Analysis · Mathematics 2018-09-28 Peter Benner , Akwum Onwunta , Martin Stoll

This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…

Numerical Analysis · Computer Science 2020-01-13 William Leeb , Vladimir Rokhlin

This paper deals with investigating numerical methods for solving coupled system of nonlinear parabolic problems. We utilize block monotone iterative methods based on Jacobi and Gauss--Seidel methods to solve difference schemes which…

Numerical Analysis · Mathematics 2019-05-10 Mohamed Al-Sultani