Elliptic systems of variable order

A numerical approach for variable-order fractional unified chaotic systems with time-delay

This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To ill...

Reduced Systems for Three-Dimensional Elliptic Equations with Variable Coefficients

We consider large sparse nonsymmetric linear systems arising from finite difference discretization of three-dimensional (3D) convection-diffusion equations with variable coefficients. We show that performing one step of cyclic reduction yields a system of equations which is well conditioned and for which fast convergence can be obtained. A certain block ordering strategy is applied, and analyti...

Homogenisation of Exponential Order for Elliptic Systems in Infinite Cylinders

Least-squares Finite Element Methods for First-order Elliptic Systems

Least-squares principles use artificial " energy " functionals to provide a Rayleigh-Ritz-like setting for the finite element method. These function-als are defined in terms of PDE's residuals and are not unique. We show that viable methods result from reconciliation of a mathematical setting dictated by the norm-equivalence of least-squares functionals with practicality constraints dictated by...

First Order Elliptic Systems : a Function Theoretic Approach

if and only if it has an entire continuation to C. In C", all entire functions, but not all holomorphic functions, or even all rational functions, are polyharmonic on their domains. Most of the book is devoted to the development and exploitation of three main tools: the serio-integral representation of a polyharmonic function on a domain in W (derived from Green's formula), the Almansi series e...