10 research outputs found
Hidden maximal monotonicity in evolutionary variational-hemivariational inequalities
In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a hidden maximal monotonicity, is used to explore the well-posedness for a class of evolutionary variational-hemivariational inequalities involving history-dependent operators and related problems with periodic and antiperiodic boundary conditions. The applicability of our theoretical results is illustrated through applications to a fractional evolution inclusion and a dynamic semipermeability problem
Uniform global attractors for non-autonomous dissipative dynamical systems
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to avoid the restrictive compactness assumptions on the space of shifts of non-autonomous terms in particular evolution problems. The results are applied to several evolution inclusions
Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise
From Crossref journal articles via Jisc Publications RouterHistory: epub 2024-01-23, issued 2024-01-23Article version: VoRPublication status: PublishedWe consider a numerical approximation for stochastic fractional differential equations driven by integrated multiplicative noise. The fractional derivative is in the Caputo sense with the fractional order α∈(0,1), and the non-linear terms satisfy the global Lipschitz conditions. We first approximate the noise with the piecewise constant function to obtain the regularized stochastic fractional differential equation. By applying Minkowski’s inequality for double integrals, we establish that the error between the exact solution and the solution of the regularized problem has an order of O(Δtα) in the mean square norm, where Δt denotes the step size. To validate our theoretical conclusions, numerical examples are presented, demonstrating the consistency of the numerical results with the established theory
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal