相关论文: Inter/extrapolation-based multirate schemes -- a d…
In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric…
Mixed superposition rules are, in short, a method to describe the general solutions of a time-dependent system of first-order differential equations, a so-called Lie system, in terms of particular solutions of other ones. This article is…
Numerical solutions to wave-type PDEs utilizing method-of-lines require the ODE solver's stability domain to include a large stretch of the imaginary axis surrounding the origin. We show here that extrapolation based solvers of…
This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…
In this work, we study decentralized convex constrained optimization problems in networks. We focus on the dual averaging-based algorithmic framework that is well-documented to be superior in handling constraints and complex communication…
The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…
In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for numerically solving initial-value…
In this paper we first present a novel operator extrapolation (OE) method for solving deterministic variational inequality (VI) problems. Similar to the gradient (operator) projection method, OE updates one single search sequence by solving…
In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper…
In radio frequency applications, electric circuits generate signals, which are amplitude modulated and/or frequency modulated. A mathematical modelling yields typically systems of differential algebraic equations (DAEs). A multivariate…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. The proposed methods are based on a specific subset of explicit one-step…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
We present a priori error estimates for a multirate time-stepping scheme for coupled differential equations. The discretization is based on Galerkin methods in time using two different time meshes for two parts of the problem. We aim at…
This paper studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Specifically we develop scalable techniques for constructing the attraction regions associated with a particular stable equilibrium,…
In this paper, some adaptive single-step methods like Trapezoid (TR), Implicit-mid point (IMP), Euler-backward (EB), and Radau IIA (Rad) methods are implemented in Maple to solve index-1 nonlinear Differential Algebraic Equations (DAEs).…
In this paper, we present a new SDC scheme for solving semi-explicit DAEs with the ability to be parallelized in which only the differential equations are numerically integrated is presented. In Shu et al. (2007) it was shown that SDC for…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…