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In this work we propose a novel approach to investigate boundary value problems (BVPs) for fully third order differential equations. It is based on the reduction of BVPs to operator equations for the nonlinear terms but not for the…

Numerical Analysis · Mathematics 2018-06-04 Dang Quang A , Dang Quang Long

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…

Numerical Analysis · Mathematics 2020-01-22 Kundan Kumar , Svetlana Kyas , Jan Nordbotten , Sergey Repin

To extract the approximate solutions in the case of nonlinear fractional order differential equations with the homogeneous and nonhomogeneous boundary conditions, the weighted residual method is embedded here. We exploit three methods such…

Numerical Analysis · Mathematics 2024-04-05 Umme Ruman , Md. Shafiqul Islam

This work presents a numerical study of functional type a posteriori error estimates for IgA approximation schemes in the context of elliptic boundary-value problems. Along with the detailed discussion of the most crucial properties of such…

Numerical Analysis · Computer Science 2018-05-28 Svetlana Matculevich

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…

Dynamical Systems · Mathematics 2023-01-04 Björn Liljegren-Sailer

The method is proposed for the study of many-point boundary value problems for systems of nonlinear ODE, by reducing them to special equivalent integral equations, and allows us [in contrast with the known method [1]] to consider boundary…

Classical Analysis and ODEs · Mathematics 2012-05-11 Yu. A. Konyaev

A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology…

Numerical Analysis · Mathematics 2021-11-30 Denys Dragunov

An a posteriori error bound for the pointwise error of the quadratic discontinuous Galerkin method for the unilateral contact problem on polygonal domain is presented. The pointwise a posteriori error analysis is based on the direct use of…

Numerical Analysis · Mathematics 2024-01-05 Rohit Khandelwal , Kamana Porwal , Tanvi Wadhawan

The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic…

Numerical Analysis · Mathematics 2014-11-12 Ulrich Langer , Sergey Repin , Monika Wolfmayr

In this study, we examine numerical approximations for 2nd-order linear-nonlinear differential equations with diverse boundary conditions, followed by the residual corrections of the first approximations. We first obtain numerical results…

Numerical Analysis · Mathematics 2023-06-19 Shovan Sourav Datta Pranta , Md. Shafiqul Islam

We present an integral equation-based method for the numerical solution of two-point boundary value systems. Special care is devoted to the mathematical formulation, namely the choice of the background Green's function that leads to a…

Numerical Analysis · Mathematics 2025-10-09 Tianze Zhang , Yixuan Ma , Jun Wang

We present an a posteriori error analysis for the mixed virtual element method (mixed VEM) applied to second order elliptic equations in divergence form with mixed boundary conditions. The resulting error estimator is of residual-type. It…

Numerical Analysis · Mathematics 2019-04-24 Andrea Cangiani , Mauricio Munar

In this work we examine a posteriori error control for post-processed approximations to elliptic boundary value problems. We introduce a class of post-processing operator that `tweaks' a wide variety of existing post-processing techniques…

Numerical Analysis · Mathematics 2023-03-01 Andreas Dedner , Jan Giesselmann , Tristan Pryer , Jennifer K Ryan

In this paper, we studied the sufficient conditions for the existence of positive solutions to the boundary value problems of Caputo fractional difference equations depending on parameters with non local boundary conditions. We construct…

Classical Analysis and ODEs · Mathematics 2020-04-03 Arif S. Bagwan , Deepak B. Pachpatte

In this work, we propose an a pointwise a posteriori error estimator for conforming finite element approximations of eigenfunctions corresponding to multiple and clustered eigenvalues of elliptic operators. It is proven that the pointwise a…

Numerical Analysis · Mathematics 2025-11-12 Zhenglei Li , Qigang Liang , Xuejun Xu

We consider the boundary value problems (BVPs) for linear secondorder ODEs with a strongly positive operator coefficient in a Banach space. The solutions are given in the form of the infinite series by means of the Cayley transform of the…

Numerical Analysis · Mathematics 2020-07-06 V. L. Makarov , N. V. Mayko

Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…

Machine Learning · Statistics 2020-03-03 Jonathan H. Huggins , Mikołaj Kasprzak , Trevor Campbell , Tamara Broderick

We establish guaranteed and practically computable a posteriori error bounds for source problems and eigenvalue problems involving linear Schr{\"o}dinger operators with atom-centered potentials discretized with linear combinations of atomic…

Numerical Analysis · Mathematics 2025-09-03 Geneviève Dusson , Mi-Song Dupuy , Ioanna-Maria Lygatsika

This paper is concerned with the derivation of conforming and non-conforming functional a posteriori error estimates for elliptic boundary value problems in exterior domains. These estimates provide computable and guaranteed upper and lower…

Numerical Analysis · Mathematics 2014-07-22 Olli Mali , Alexey Muzalevskiy , Dirk Pauly

This work reviews goal-oriented a posteriori error control, adaptivity and solver control for finite element approximations to boundary and initial-boundary value problems for stationary and non-stationary partial differential equations,…

Numerical Analysis · Mathematics 2024-12-02 Bernhard Endtmayer , Ulrich Langer , Thomas Richter , Andreas Schafelner , Thomas Wick