Related papers: Operator splittings and spatial approximations for…
We introduce a new iterative method to recover a real compact supported potential of the Schr\"odinger operator from their fixed angle scattering data. The method combines a fixed point argument with a suitable approximation of the…
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system…
In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of the second kind to obtain results of existence, regularity…
We approximate the solution for the time dependent Schr\"odinger equation (TDSE) in two steps. We first use a pseudo-spectral collocation method that uses samples of functions on rank-1 or rank-r lattice points with unitary Fourier…
In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…
I propose a large class of stochastic Markov processes associated with probability distributions analogous to that of lattice gauge theory with dynamical fermions. The construction incorporates the idea of approximate spectral split of the…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
Vlasov equations model the dynamics of plasma in the collisionless regime. A standard approach for numerically solving the Vlasov equation is to operator split the spatial and velocity derivative terms, allowing simpler time-stepping…
The purpose of this paper is concerned with the approximate solution of split equality problems. We introduce two types of algorithms and a new self-adaptive stepsize without prior knowledge of operator norms. The corresponding strong…
In this paper 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. With the idea of coordinate descent, we design a…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
This paper investigates the possibility of approximating multiple mathematical operations in latent space for expression derivation. To this end, we introduce different multi-operational representation paradigms, modelling mathematical…
In this paper, we discuss the different splitting approaches to solve the Gross-Pitaevskii equation numerically. We consider conservative finite-difference schemes and spectral methods for the spatial discretisation. Further, we apply…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
We consider evolutionary equations as introduced by R.\ Picard in 2009 and develop a general theory for approximation which can be seen as a theoretical foundation for numerical analysis for evolutionary equations. To demonstrate the…