A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation

@inproceedings{Ilic2009ANS,
title={A Numerical Solution Using an Adaptively Preconditioned Lanczos Method for a Class of Linear Systems Related with the Fractional Poisson Equation},
author={Milos Ilic and Ian W. Turner and Vo Anh},
year={2009}
}

This study considers the solution of a class of linear systems related with the fractional Poisson equation FPE −∇2 φ g x, y with nonhomogeneous boundary conditions on a bounded domain. A numerical approximation to FPE is derived using a matrix representation of the Laplacian to generate a linear system of equations with its matrix A raised to the fractional power α/2. The solution of the linear system then requires the action of the matrix function f A A−α/2 on a vector b. For large, sparse… CONTINUE READING