55 citations · 82 across the 9 of their papers we have counts for
14 papers
Analysis of numerical methods for spectral fractional elliptic equations based on the best uniform rational approximation
Stanislav Harizanov, Raytcho Lazarov, Pencho Marinov +2
Here we study theoretically and compare experimentally an efficient method for solving systems of algebraic equations, where the matrix comes from the discretization of a fractiona…
Comparison analysis on two numerical methods for fractional diffusion problems based on rational approximations of
Stanislav Harizanov, Raytcho Lazarov, Pencho Marinov +2
We discuss, study, and compare experimentally three methods for solving the system of algebraic equations , , where is a symmetric a…
On Sinc Quadrature Approximations of Fractional Powers of Regularly Accretive Operators
Andrea Bonito, Wenyu Lei, Joseph E. Pasciak
We consider the finite element approximation of fractional powers of regularly accretive operators via the Dunford-Taylor integral approach. We use a sinc quadrature scheme to appr…
Space-Time Petrov-Galerkin FEM for Fractional Diffusion Problems
Beiping Duan, Bangti Jin, Raytcho Lazarov +2
We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order $α\i…
Numerical Approximation of the Integral Fractional Laplacian
Andrea Bonito, Wenyu Lei, Joseph E. Pasciak
We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral represen…
Numerical Approximation of Space-time Fractional Parabolic Equations
Andrea Bonito, Wenyu Lei, Joseph E. Pasciak
In this paper, we develop a numerical scheme for the space-time fractional parabolic equation, i.e., an equation involving a fractional time derivative and a fractional spatial ope…
The Approximation of Parabolic Equations Involving Fractional Powers of Elliptic Operators
Andrea Bonito, Wenyu Lei, Joseph E. Pasciak
We study the numerical approximation of a time dependent equation involving fractional powers of an elliptic operator defined to be the unbounded operator associated with a Her…
Numerical Approximation of Fractional Powers of Regularly Accretive Operators
Andrea Bonito, Joseph E. Pasciak
We study the numerical approximation of fractional powers of accretive operators in this paper. Namely, if is the accretive operator associated with an accretive sesquilinear f…
Error Analysis of Finite Element Methods for Space-Fractional Parabolic Equations
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
We consider an initial/boundary value problem for one-dimensional fractional-order parabolic equations with a space fractional derivative of Riemann-Liouville type and order $α\in…
A Finite Element Method for the Fractional Sturm-Liouville Problem
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $α\…
Variational formulation of problems involving fractional order differential operators
Bangti Jin, Raytcho Lazarov, Joseph Pasciak
In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order on the unit interval . These fractional…
Error Analysis of Semidiscrete Finite Element Methods for Inhomogeneous Time-Fractional Diffusion
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
We consider the initial boundary value problem for the inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and a nonsmooth right hand s…
Numerical Approximation of Fractional Powers of Elliptic Operators
Andrea Bonito, Joseph E. Pasciak
We present and study a novel numerical algorithm to approximate the action of where is a symmetric and positive definite unbounded operator on a Hilbert space $H_…
Galerkin FEM for fractional order parabolic equations with initial data in
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
We investigate semi-discrete numerical schemes based on the standard Galerkin and lumped mass Galerkin finite element methods for an initial-boundary value problem for homogeneous…