Related papers: Operator splittings and spatial approximations for…
Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions $\varphi_j$ and a sequence of distributions/functions $\widetilde{\varphi}_j$. Error…
We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree $p$ with $k$ continuous derivatives. The construction is based on polynomial extension from neighboring elements…
The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…
We propose an operational method for the solution of differential equations involving vector products. The technique we propose is based on the use of the evolution operator, defined in such a way that the wealth of techniques developed…
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the $H^{-1}$-gradient flow of the…
Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…
We consider the Cauchy problem for stochastic fractional evolution equations with Caputo time fractional derivative of order $1<\alpha<2$ and space variable coefficients on an unbounded domain. The space derivatives that appear in the…
We present a new method to solve in a semianalytical way the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at NLO order in the x-space. The method allows to construct an evolution operator expressed in form of a rapidly…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
We propose a methodology for studying the performance of common splitting methods through semidefinite programming. We prove tightness of the methodology and demonstrate its value by presenting two applications of it. First, we use the…
The Chernoff approximation method is a powerful and flexible tool of functional analysis, which allows in many cases to express exp(tL) in terms of variable coefficients of a linear differential operator L. In this paper, we prove a theorem…
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular schemes are constructed via setup and solution of polynomial…
We consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators,…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
This work is devoted to establish the strong convergence results of an iterative algorithm generated by the shrinking projection method in Hilbert spaces. The proposed approximation sequence is used to find a common element in the set of…
In this paper we consider splitting methods for nonlinear ordinary differential equations in which one of the (partial) flows that results from the splitting procedure can not be computed exactly. Instead, we insert a well-chosen state…