Related papers: Spectral Approximation to Fractional Integral Oper…
Exponential time integrators have been applied successfully in several physics-related differential equations. However, their application in hyperbolic systems with absorbing boundaries, like the ones arising in seismic imaging, still lacks…
We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the…
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
Fractional order controllers become increasingly popular due to their versatility and superiority in various performance. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.…
Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the self-adjoint…
We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…
We consider a fast approximation method for a solution of a certain stochastic non-local pseudodifferential equation. This equation defines a Mat\'ern class random field. The approximation method is based on the spectral compactness of the…
In this paper we consider an orthonormal basis, generated by a tensor product of Fourier basis functions, half period cosine basis functions, and the Chebyshev basis functions. We deal with the approximation problem in high dimensions…
We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
The low-rank matrix approximation problem is ubiquitous in computational mathematics. Traditionally, this problem is solved in spectral or Frobenius norms, where the accuracy of the approximation is related to the rate of decrease of the…
Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
We present the Fast Chebyshev Transform (FCT), a fast, randomized algorithm to compute a Chebyshev approximation of functions in high-dimensions from the knowledge of the location of its nonzero Chebyshev coefficients. Rather than sampling…
Modeling spectral line profiles taking frequency redistribution effects into account is a notoriously challenging problem from the computational point of view, especially when polarization phenomena (atomic polarization and polarized…
In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…
It is well known that for every $f\in C^m$ there exists a polynomial $p_n$ such that $p^{(k)}_n\rightarrow f^{(k)}$, $k=0,\ldots,m$. Here we prove such a result for fractional (non-integer) derivatives. Moreover, a numerical method is…