In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by fractional diffusion equation. Multigrid methods within the all-at-once approach to solve first order optimality Karush–Kuhn–Tucker (KKT) systems are widely popular, but their development have relied on underlying being sparse. On other hand, most discretizations, matrix represe...

BACKGROUND The NO--cGMP system plays a key role in the regulation of sinusoidal tonus and liver blood flow with phosphodiesterase-5 (PDE-5) terminating the dilatory action of cGMP. We, therefore, investigated the effects of PDE-5 inhibitors on hepatic and systemic hemodynamics in rats. METHODS Hemodynamic parameters were monitored for 60 min. after intravenous injection of sildenafil and vard...

In this work, numerical solution of multi term space fractional PDE is calculated by using radial basis functions. The derivatives functions are evaluated Caputo and Riemann-Liouville definitions. Local applied to get stable accurate the problem. Accuracy method assessed double mesh procedure. Numerical solutions presented for different orders show effect introducing fractionality.

Abstract

The aim of this paper is to study a conservative wave equation coupled to a diffusion equation : this coupled system naturally arises in musical acoustics when viscous and thermal effects at the wall of the duct of a wind instrument are taken into account. The resulting equation, known as Webster-Lokshin model, has variable coefficients in space, and a fractional derivative in time. The port-Ha...

The spine of an object is an entity that can characterise the object’s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown th...

in this paper, a numerical efficient method is proposed for the solution of time fractionalmobile/immobile equation. the fractional derivative of equation is described in the caputosense. the proposed method is based on a finite difference scheme in time and legendrespectral method in space. in this approach the time fractional derivative of mentioned equationis approximated by a scheme of order o...

This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for s...