Detailed Error Analysis for a Fractional Adams Method

Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation

We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann–Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank...

A Meshless Method for Numerical Solution of Fractional Differential Equations

In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...

Generalized Adams Product Quadrature Rules for Fractional Differential Equations

An initial value problem for a Fractional Differential Equation (FDE) can be reformulated as a Volterra integral equation of the second kind with weakly singular kernel. Its solution can be approximated by applying suitable convolution quadratures. Methods of this type currently available in the literature are, for example, Adams product quadrature rules or Fractional Linear Multistep Methods, ...

A PDE approach to fractional diffusion: A posteriori error analysis

We derive a computable a posteriori error estimator for the αharmonic extension problem, which localizes the fractional powers of elliptic operators supplemented with Dirichlet boundary conditions. Our a posteriori error estimator relies on the solution of small discrete problems on anisotropic cylindrical stars. It exhibits built-in flux equilibration and is equivalent to the energy error up t...